Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

A Study on Aerosol Transport Dynamics over the Indian Landmass and the Adjoining Oceanic Regions Using Satellite Data

The present study brings out the influence of transport dynamics on the aerosol distribution over the Indian region at a few selected geographically distinct locations. Over the Bay of Bengal the dominant pathway of aerosol transport during the pre-monsoon period is through higher altitudes (~ 3 km); directed from the Indian main land. In contrast, the aerosol pathways over the Arabian Sea during the same period are quite complex. They are directed from geographically different environments around the ocean through different altitudes. However in general, the day-to-day variability of AOD at both these regions is significantly influenced by the features of atmospheric circulation especially, the wind convergence at higher altitudes (around 3 km). Over the Ganga Basin during the winter period, the wind convergence at lower altitudes (< I km) govems the shon term variations in AOD, while the mean AOD distribution at this location is mainly governed by the local anthropogenic sources.

Targeted Public Distribution System in Food Grains:Extent of Utlization by the Tribal Population in Kerala

In India, Food Security meant supply of food grains and the medium was Public Distribution System. Public Distribution System (PDS) is a rationing mechanism that entitles households to specified quantities of selected commodities at subsidized prices. The Objectives of PDS are maintaining Price Stability, rationing during times of scarcity, welfare of the poor, and keeping a check on private trade. Kerala has registered remarkable improvement in poverty reduction in general over the years among all social sections, including scheduled caste and scheduled tribe population. As part of the structural adjustment intended to reduce public expenditure, PDS has been modified as Revamped PDS (RPDS) during 1992 and later on as Targeted PDS (TPDS) in 1997, intended to target households on the basis of income criterion, classifying people as Below Poverty Line (BPL) and Above Poverty Line (APL). TPDS provides 25Kg. of food gra.ins through the Fair Price Shops per month @ Rs.3/- per Kg. of rice/ wheat to the BPL category and @Rs.8.90 and Rs.6.7O for rice and wheat respectively to the APL category of people. Since TPDS is intended to target the poor people, the subsidy spent by the government for the scheme should be beneficial to the poor people and naturally they should utilize the benefits by purchasing the food grains allotted under the scheme. Several studies have shown that there is underutilization of the allotments under TPDS. Therefore, the extent of utilization of TPDS in food grains, how and why remains as a major hurdle, in improving the structure and system of PDS. Livelihood of the tribal population being under threat due to increasing degradation of the resources, the targeting system ought to be effective among the tribal population. Therefore, performance of the TPDS in food grains, in terms of the utilization by the tribal population in Kerala, impact thereof and the factors, if any, affecting proper utilization were considered as the research problem in this study. The study concentrated on the pattern of consumption of food grains by the tribal people, whether their hunger needs are met by distribution of food grains through the TPDS, extent to which TPDS in food grains reduce their share of expenditure on food in the total household expenditure, and the factors affecting the utilization of the TPDS in food grains by the tribal population. Going through the literature, it has been noted that only few studies concentrated on the utilization of TPDS in food grains among the tribal population in Kerala.The Research Design used in this study is descriptive in nature, but exploratory in some aspects. Idukki, Palakkad and Wayanad have more than 60% of the population of the tribals in the state. Within the three districts mentioned above, 14 villages with scheduled tribe concentration were selected for the study. 95 tribal colonies were selected from among the various tribal settlements. Collection of primary data was made from 1231 households with in the above tribal colonies. Analysis of data on the socio-economic factors of the tribal people, pattern of food consumption, extent of reduction in the share of expenditure on food among the household expenditure of the tribal people and the impact of TPDS on the tribal families etc. and testing of hypotheses to find out the relation/association of each of the six variables, using the data on BPL and APL categories of households separately have resulted in findings such as six percent of the tribal families do not have Ration Cards, average per capita consumption of food grains by the tribal people utilizing TPDS meets 62% of their minimum requirement, whereas the per capita consumption of food grains by the tribal people is higher than the national average per capita consumption, 63% deficiency in food grains may be felt by tribal people in general, if TPDS is withdrawn, and the deficit for BPL tribal people may be 82%, TPDS facilitates a reduction of 9.71% in the food expenditure among the total household expenditure of the tribal people in general, share of food to non-food among BPL category of tribals is 55:45 and 40:60 among the APL, Variables, viz. household income, number of members in the family and distance of FPS from tribal settlements etc. have influence on the quantity of rice being purchased by the tribal people from the Fair Price Shops, and there is influence of household income and distance of FPS from tribal settlements on the quantity of rice being purchased by the tribal people from the open market. Rationing with differential pricing on phased allotments, rectification of errors in targeting, anomalies in norms and procedures for classifying tribal people as BPL/APL, exclusive Income Generation for tribal population, paddy cultivation in the landholdings possessed by the tribal people, special drive for allotment of Ration Cards to the tribal people, especially those belonging to the BPL category, Mobile Fair Price Shops in tribal settlements, ensure quality of the food grains distributed through the TPDS, distribution of wheat flour in packed condition instead of wheat through the Fair Price Shops are recommended to address the shortcomings and weaknesses of the TPDS vis-avis the tribal population in Kerala.

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Systematics, Germplasm evaluation and pattern of distribution and abundance of freshwater fishes of Kerala (lndia)

The overall focus of the thesis involves the systematics,germplasm evaluation and pattern of distribution and abundance of freshwater fishes of kerala (india).Biodiversity is the measure of variety of Life.With the signing on the convention on biodiversity, the countries become privileged with absolute rights and responsibility to conserve and utilize their diverse resources for the betterment of mankind in a sustainable way. South-east Asia along with Africa and South America were considered to be the most biodiversity rich areas in the world .The tremendous potential associated with the sustainable utilization of fish germplasm resources of various river systems of Kerala for food, aquaculture and ornamental purposes have to be fully tapped for economic upliftment of fisherman community and also for equitable sharing of benefits among the mankind without compromising the conservation of the rare and unique fish germplasm resources for the future generations.The study was carried during April 2000 to December 2004. 25 major river systems of Kerala were surveyed for fish fauna for delineating the pattern of distribution and abundance of fishes both seasonally and geographically.The results of germplasm inventory and evaluation of fish species were presented both for the state and also river wise. The results of evaluation of fish species for their commercial utilization revealed that, of the 145, 76 are ornamental, 47 food and 22 cultivable. 21 species are strictly endemic to Kerala rivers. The revalidation on biodiversity status of the fishes assessed based on IUCN is so alarming that a high percentage of fishes (59spp.) belong to threatened category which is inclusive of 8 critically ndangered (CR), 36 endangered and 15 species under vulnerable (VU) category.The river wise fish germplasm inventory surveys were conducted in 25 major river systems of Kerala.The results of the present study is indicative of existence of several new fish species in the streams and rivulets located in remote areas of the forests and therefore, new exclusive surveys are required to surface fish species new to science, new distributional records etc, for the river systems.The results of fish germplasm evaluation revealed that there exist many potential endemic ornamental and cultivable fishes in Kerala. It is found imperative to utilize these species sustainably for improving the aquaculture production and aquarium trade of the country which would definitely fetch more income and generate employment.

‘Reliability Concepts in Quantile-based Analysis of Lifetime Data

Reliability analysis is a well established branch of statistics that deals with the statistical study of different aspects of lifetimes of a system of components. As we pointed out earlier that major part of the theory and applications in connection with reliability analysis were discussed based on the measures in terms of distribution function. In the beginning chapters of the thesis, we have described some attractive features of quantile functions and the relevance of its use in reliability analysis. Motivated by the works of Parzen (1979), Freimer et al. (1988) and Gilchrist (2000), who indicated the scope of quantile functions in reliability analysis and as a follow up of the systematic study in this connection by Nair and Sankaran (2009), in the present work we tried to extend their ideas to develop necessary theoretical framework for lifetime data analysis. In Chapter 1, we have given the relevance and scope of the study and a brief outline of the work we have carried out. Chapter 2 of this thesis is devoted to the presentation of various concepts and their brief reviews, which were useful for the discussions in the subsequent chapters .In the introduction of Chapter 4, we have pointed out the role of ageing concepts in reliability analysis and in identifying life distributions .In Chapter 6, we have studied the first two L-moments of residual life and their relevance in various applications of reliability analysis. We have shown that the first L-moment of residual function is equivalent to the vitality function, which have been widely discussed in the literature .In Chapter 7, we have defined percentile residual life in reversed time (RPRL) and derived its relationship with reversed hazard rate (RHR). We have discussed the characterization problem of RPRL and demonstrated with an example that the RPRL for given does not determine the distribution uniquely

Bionomics, Resource Characteristics And Distribution Of The Threatened Freshwater Fishes Of Kerala

The previous faunistic studies were concentrated.on the taxonomical and zoogeo— graphical aspects. These studies contributed to many new additions to the fish fauna of Kerala meanwhile many species described earlier are reported missing in recent years. Many fish species were collected only once or twice by scientists. Detailed information on distribution, habitat, feeding habits, reproduction, population size, etc. are available only with regard to a very few fish species. A meaningful assessment on the biodiversity status of the majority of freshwater fishes cannot be done for want of sufficient data base and therefore, no suitable conservation and management programmes are forthcoming for the protection and preservation of the unique fish germplasm resources of Kerala. The present study was conceptualised and undertaken mostly aiming at bridging these gaps by generating an authentic data base on the distribution, resource characteristics and bionomics of the threatened fishes inhabiting the rivers of Kerala. Osteobrama bakeri (Day) is an endemic fish having a very highly restricted and fragmented distribution in Periyar, Chalakudy, Kabini, Kallada and Meenachil rivers of Kerala. This belongs to vulnerable category and is locally known as Mullanpaval which is valued as food fish. Besides, due to its vibrant and attractive colouration and easiness for domestication, it has great potential for being propagated as an ornamental fish. Hitherto, no information is available on the bionomics and resource characteristics of this species. Studies on detailed life history traits are indispensable for fishery management, development of captive breeding technique and implementation of various conservation programmes. In the present study, a pioneer attempt is also made to investigate the life history traits, resource characteristics, proximate composition, etc. of O.baken'.

The Systematics, Distribution and Bionomics of Deep sea fishes beyond depth 200m along the South west coast of India

Reducing fishing pressure in coastal waters is the need of the day in the Indian marine fisheries sector of the country which is fast changing from a mere vocational activity to a capital intensive industry. It requires continuous monitoring of the resource exploitation through a scientifically acceptable methodology, data on production of each species stock, the number and characteristics of the fishing gears of the fleet, various biological characteristics of each stock, the impact of fishing on the environment and the role of fishery—independent on availability and abundance. Besides this, there are issues relating to capabilities in stock assessment, taxonomy research, biodiversity, conservation and fisheries management. Generation of reliable data base over a fixed time frame, their analysis and interpretation are necessary before drawing conclusions on the stock size, maximum sustainable yield, maximum economic yield and to further implement various fishing regulatory measures. India being a signatory to several treaties and conventions, is obliged to carry out assessments of the exploited stocks and manage them at sustainable levels. Besides, the nation is bound by its obligation of protein food security to people and livelihood security to those engaged in marine fishing related activities. Also, there are regional variabilities in fishing technology and fishery resources. All these make it mandatory for India to continue and strengthen its marine capture fisheries research in general and deep sea fisheries in particular. Against this background, an attempt is made to strengthen the deep sea fish biodiversity and also to generate data on the distribution, abundance, catch per unit effort of fishery resources available beyond 200 m in the EEZ of southwest coast ofIndia and also unravel some of the aspects of life history traits of potentially important non conventional fish species inhabiting in the depth beyond 200 m. This study was carried out as part of the Project on Stock Assessment and Biology of Deep Sea Fishes of Indian EEZ (MoES, Govt. of India).

“Population Characteristics, Fishery and Post larval distribution of Macrobrachium rosenbergii (de Man) and M. idella (Hilgendorf) of Vembanad lake”

Macrobrachium rosenbergii (de Man) and M.ide77a (Hilgendorf) form two commercially important Palaemonid prawns of the Vembanad lake (9 28' and 10 10’ N and 76 13' and 76 31' E). Both of them were known to have contributed to a very lucrative fishery during the sixties, however, in recent years these natural resources have badly depleted owing to the impact of many man made alterations brought about in the ecosystem such as habitat reduction, physical obstruction imposed in the migratory pathway of these species, pollution hazards, etc,. Changed environmental conditions and increased fishing pressures caused persistent alterations in the stock size of these prawns during the past so many years, however, no serious attempt was made to monitor the stock size from time to time and also to bring out the resource characteristics. Though, the morphotypic differentiation in grow out male population of M.rosenbergii has been documented, no similar studies were conducted with regard to natural male and female population. Based on the data collected during fishery cruise surveys conducted in Vembanad lake from March '94 to February '96, population characteristics. postlarval distribution, fishery and population dynamics of M.rosenbergii and M.ide77a of the lake were studied in detail.

Studies on the horizontal and vertical distribution of clouds and their impact on energetics of the Atmosphere over the Indian Region

Motivation for the present study is to improve the scienti c understanding on the prominent gap areas in the average three-dimensional distribution of clouds and their impact on the energetics of the earth-atmosphere system. This study is focused on the Indian subcontinent and the surrounding oceans bound within the latitude-longitude bands of 30 S to 30 N and 30 E to 110 E. Main objectives of this study are to : (i) estimate the monthly and seasonal mean vertical distributions of clouds and their spatial variations (which provide the monthly and seasonal mean 3-dimensional distributions of clouds) using multi-year satellite data and investigate their association with the general circulation of the atmosphere, (ii) investigate the characteristics of the `pool of inhibited cloudiness' that appear over the southwest Bay of Bengal during the Asian summer monsoon season (revealed by the 3-dimensional distribution of clouds) and identify the potential mechanisms for its genesis, (iii) investigate the role of SST and atmospheric thermo-dynamical parameters in regulating the vertical development and distribution of clouds, (iv) investigate the vertical distribution of tropical cirrus clouds and their descending nature using lidar observations at Thiruvananthapuram (8.5 N, 77 E), a tropical coastal station at the southwest Peninsular India, and (v) assessment of the impact of clouds on the energetics of the earth-atmosphere system, by estimating the regional seasonal mean cloud radiative forcing at top-of-the-atmosphere (TOA) and latent heating of the atmosphere by precipitating clouds using satellite data

‘Modeling and Analysis of Competing Risks Data’

there has been much research on analyzing various forms of competing risks data. Nevertheless, there are several occasions in survival studies, where the existing models and methodologies are inadequate for the analysis competing risks data. ldentifiabilty problem and various types of and censoring induce more complications in the analysis of competing risks data than in classical survival analysis. Parametric models are not adequate for the analysis of competing risks data since the assumptions about the underlying lifetime distributions may not hold well. Motivated by this, in the present study. we develop some new inference procedures, which are completely distribution free for the analysis of competing risks data.

Development of hybrid UV VCSEL with organic active material and dielectric DBR mirrors for medical, sensoric and data storage applications

Lasers play an important role for medical, sensoric and data storage devices. This thesis is focused on design, technology development, fabrication and characterization of hybrid ultraviolet Vertical-Cavity Surface-Emitting Lasers (UV VCSEL) with organic laser-active material and inorganic distributed Bragg reflectors (DBR). Multilayer structures with different layer thicknesses, refractive indices and absorption coefficients of the inorganic materials were studied using theoretical model calculations. During the simulations the structure parameters such as materials and thicknesses have been varied. This procedure was repeated several times during the design optimization process including also the feedback from technology and characterization. Two types of VCSEL devices were investigated. The first is an index coupled structure consisting of bottom and top DBR dielectric mirrors. In the space in between them is the cavity, which includes active region and defines the spectral gain profile. In this configuration the maximum electrical field is concentrated in the cavity and can destroy the chemical structure of the active material. The second type of laser is a so called complex coupled VCSEL. In this structure the active material is placed not only in the cavity but also in parts of the DBR structure. The simulations show that such a distribution of the active material reduces the required pumping power for reaching lasing threshold. High efficiency is achieved by substituting the dielectric material with high refractive index for the periods closer to the cavity. The inorganic materials for the DBR mirrors have been deposited by Plasma- Enhanced Chemical Vapor Deposition (PECVD) and Dual Ion Beam Sputtering (DIBS) machines. Extended optimizations of the technological processes have been performed. All the processes are carried out in a clean room Class 1 and Class 10000. The optical properties and the thicknesses of the layers are measured in-situ by spectroscopic ellipsometry and spectroscopic reflectometry. The surface roughness is analyzed by atomic force microscopy (AFM) and images of the devices are taken with scanning electron microscope (SEM). The silicon dioxide (SiO2) and silicon nitride (Si3N4) layers deposited by the PECVD machine show defects of the material structure and have higher absorption in the ultra violet range compared to ion beam deposition (IBD). This results in low reflectivity of the DBR mirrors and also reduces the optical properties of the VCSEL devices. However PECVD has the advantage that the stress in the layers can be tuned and compensated, in contrast to IBD at the moment. A sputtering machine Ionsys 1000 produced by Roth&Rau company, is used for the deposition of silicon dioxide (SiO2), silicon nitride (Si3N4), aluminum oxide (Al2O3) and zirconium dioxide (ZrO2). The chamber is equipped with main (sputter) and assisted ion sources. The dielectric materials were optimized by introducing additional oxygen and nitrogen into the chamber. DBR mirrors with different material combinations were deposited. The measured optical properties of the fabricated multilayer structures show an excellent agreement with the results of theoretical model calculations. The layers deposited by puttering show high compressive stress. As an active region a novel organic material with spiro-linked molecules is used. Two different materials have been evaporated by utilizing a dye evaporation machine in the clean room of the department Makromolekulare Chemie und Molekulare Materialien (mmCmm). The Spiro-Octopus-1 organic material has a maximum emission at the wavelength λemission = 395 nm and the Spiro-Pphenal has a maximum emission at the wavelength λemission = 418 nm. Both of them have high refractive index and can be combined with low refractive index materials like silicon dioxide (SiO2). The sputtering method shows excellent optical quality of the deposited materials and high reflection of the multilayer structures. The bottom DBR mirrors for all VCSEL devices were deposited by the DIBS machine, whereas the top DBR mirror deposited either by PECVD or by combination of PECVD and DIBS. The fabricated VCSEL structures were optically pumped by nitrogen laser at wavelength λpumping = 337 nm. The emission was measured by spectrometer. A radiation of the VCSEL structure at wavelength 392 nm and 420 nm is observed.

Estimators and Tests based on Likelihood-Depth with Application to Weibull Distribution, Gaussian and Gumbel Copula

In dieser Arbeit werden mithilfe der Likelihood-Tiefen, eingeführt von Mizera und Müller (2004), (ausreißer-)robuste Schätzfunktionen und Tests für den unbekannten Parameter einer stetigen Dichtefunktion entwickelt. Die entwickelten Verfahren werden dann auf drei verschiedene Verteilungen angewandt. Für eindimensionale Parameter wird die Likelihood-Tiefe eines Parameters im Datensatz als das Minimum aus dem Anteil der Daten, für die die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, und dem Anteil der Daten, für die diese Ableitung nicht positiv ist, berechnet. Damit hat der Parameter die größte Tiefe, für den beide Anzahlen gleich groß sind. Dieser wird zunächst als Schätzer gewählt, da die Likelihood-Tiefe ein Maß dafür sein soll, wie gut ein Parameter zum Datensatz passt. Asymptotisch hat der Parameter die größte Tiefe, für den die Wahrscheinlichkeit, dass für eine Beobachtung die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, gleich einhalb ist. Wenn dies für den zu Grunde liegenden Parameter nicht der Fall ist, ist der Schätzer basierend auf der Likelihood-Tiefe verfälscht. In dieser Arbeit wird gezeigt, wie diese Verfälschung korrigiert werden kann sodass die korrigierten Schätzer konsistente Schätzungen bilden. Zur Entwicklung von Tests für den Parameter, wird die von Müller (2005) entwickelte Simplex Likelihood-Tiefe, die eine U-Statistik ist, benutzt. Es zeigt sich, dass für dieselben Verteilungen, für die die Likelihood-Tiefe verfälschte Schätzer liefert, die Simplex Likelihood-Tiefe eine unverfälschte U-Statistik ist. Damit ist insbesondere die asymptotische Verteilung bekannt und es lassen sich Tests für verschiedene Hypothesen formulieren. Die Verschiebung in der Tiefe führt aber für einige Hypothesen zu einer schlechten Güte des zugehörigen Tests. Es werden daher korrigierte Tests eingeführt und Voraussetzungen angegeben, unter denen diese dann konsistent sind. Die Arbeit besteht aus zwei Teilen. Im ersten Teil der Arbeit wird die allgemeine Theorie über die Schätzfunktionen und Tests dargestellt und zudem deren jeweiligen Konsistenz gezeigt. Im zweiten Teil wird die Theorie auf drei verschiedene Verteilungen angewandt: Die Weibull-Verteilung, die Gauß- und die Gumbel-Copula. Damit wird gezeigt, wie die Verfahren des ersten Teils genutzt werden können, um (robuste) konsistente Schätzfunktionen und Tests für den unbekannten Parameter der Verteilung herzuleiten. Insgesamt zeigt sich, dass für die drei Verteilungen mithilfe der Likelihood-Tiefen robuste Schätzfunktionen und Tests gefunden werden können. In unverfälschten Daten sind vorhandene Standardmethoden zum Teil überlegen, jedoch zeigt sich der Vorteil der neuen Methoden in kontaminierten Daten und Daten mit Ausreißern.

Modelling structural zeros in compositional data

This analysis was stimulated by the real data analysis problem of household expenditure data. The full dataset contains expenditure data for a sample of 1224 households. The expenditure is broken down at 2 hierarchical levels: 9 major levels (e.g. housing, food, utilities etc.) and 92 minor levels. There are also 5 factors and 5 covariates at the household level. Not surprisingly, there are a small number of zeros at the major level, but many zeros at the minor level. The question is how best to model the zeros. Clearly, models that try to add a small amount to the zero terms are not appropriate in general as at least some of the zeros are clearly structural, e.g. alcohol/tobacco for households that are teetotal. The key question then is how to build suitable conditional models. For example, is the sub-composition of spending excluding alcohol/tobacco similar for teetotal and non-teetotal households? In other words, we are looking for sub-compositional independence. Also, what determines whether a household is teetotal? Can we assume that it is independent of the composition? In general, whether teetotal will clearly depend on the household level variables, so we need to be able to model this dependence. The other tricky question is that with zeros on more than one component, we need to be able to model dependence and independence of zeros on the different components. Lastly, while some zeros are structural, others may not be, for example, for expenditure on durables, it may be chance as to whether a particular household spends money on durables within the sample period. This would clearly be distinguishable if we had longitudinal data, but may still be distinguishable by looking at the distribution, on the assumption that random zeros will usually be for situations where any non-zero expenditure is not small. While this analysis is based on around economic data, the ideas carry over to many other situations, including geological data, where minerals may be missing for structural reasons (similar to alcohol), or missing because they occur only in random regions which may be missed in a sample (similar to the durables)

The allometry of non-employment. What can compositional data analysis tell us about labour market performance across the UK's regions?

The low levels of unemployment recorded in the UK in recent years are widely cited as evidence of the country’s improved economic performance, and the apparent convergence of unemployment rates across the country’s regions used to suggest that the longstanding divide in living standards between the relatively prosperous ‘south’ and the more depressed ‘north’ has been substantially narrowed. Dissenters from these conclusions have drawn attention to the greatly increased extent of non-employment (around a quarter of the UK’s working age population are not in employment) and the marked regional dimension in its distribution across the country. Amongst these dissenters it is generally agreed that non-employment is concentrated amongst older males previously employed in the now very much smaller ‘heavy’ industries (e.g. coal, steel, shipbuilding). This paper uses the tools of compositiona l data analysis to provide a much richer picture of non-employment and one which challenges the conventional analysis wisdom about UK labour market performance as well as the dissenters view of the nature of the problem. It is shown that, associated with the striking ‘north/south’ divide in nonemployment rates, there is a statistically significant relationship between the size of the non-employment rate and the composition of non-employment. Specifically, it is shown that the share of unemployment in non-employment is negatively correlated with the overall non-employment rate: in regions where the non-employment rate is high the share of unemployment is relatively low. So the unemployment rate is not a very reliable indicator of regional disparities in labour market performance. Even more importantly from a policy viewpoint, a significant positive relationship is found between the size of the non-employment rate and the share of those not employed through reason of sickness or disability and it seems (contrary to the dissenters) that this connection is just as strong for women as it is for men