An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Planar homography: accuracy analysis and applications

Projective homography sits at the heart of many problems in image registration. In addition to many methods for estimating the homography parameters (R.I. Hartley and A. Zisserman, 2000), analytical expressions to assess the accuracy of the transformation parameters have been proposed (A. Criminisi et al., 1999). We show that these expressions provide less accurate bounds than those based on the earlier results of Weng et al. (1989). The discrepancy becomes more critical in applications involving the integration of frame-to-frame homographies and their uncertainties, as in the reconstruction of terrain mosaics and the camera trajectory from flyover imagery. We demonstrate these issues through selected examples

Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of beingcompositional data and, for a given level of significance, are likely to be beyond thecapabilities of laboratories to distinguish between minute concentrations and completeabsence, thus preventing laboratories from reporting extremely low concentrations of theanalyte. Instead, what is reported is the detection limit, which is the minimumconcentration that conclusively differentiates between presence and absence of theelement. A spatially distributed exhaustive sample is employed in this study to generateunbiased sub-samples, which are further censored to observe the effect that differentdetection limits and sample sizes have on the inference of population distributionsstarting from geochemical analyses having specimens below detection limit (nondetects).The isometric logratio transformation is used to convert the compositional data in thesimplex to samples in real space, thus allowing the practitioner to properly borrow fromthe large source of statistical techniques valid only in real space. The bootstrap method isused to numerically investigate the reliability of inferring several distributionalparameters employing different forms of imputation for the censored data. The casestudy illustrates that, in general, best results are obtained when imputations are madeusing the distribution best fitting the readings above detection limit and exposes theproblems of other more widely used practices. When the sample is spatially correlated, itis necessary to combine the bootstrap with stochastic simulation

Accuracy in the experimental calorimetric study of the crystallization kinetics and predicitve transformation diagrams: Application to a Ga-Te amorphous alloy

The uncertainties inherent to experimental differential scanning calorimetric data are evaluated. A new procedure is developed to perform the kinetic analysis of continuous heating calorimetric data when the heat capacity of the sample changes during the crystallization. The accuracy of isothermal calorimetric data is analyzed in terms of the peak-to-peak noise of the calorimetric signal and base line drift typical of differential scanning calorimetry equipment. Their influence in the evaluation of the kinetic parameters is discussed. An empirical construction of the time-temperature and temperature heating rate transformation diagrams, grounded on the kinetic parameters, is presented. The method is applied to the kinetic study of the primary crystallization of Te in an amorphous alloy of nominal composition Ga20Te80, obtained by rapid solidification.

Identification of new transformation products during enzymatic treatment of tetracycline and erythromycin antibiotics at laboratory scale by an on-line turbulent flow liquid-chromatography coupled to a high resolution mass spectrometer LTQ-Orbitrap

This work describes the formation of transformation products (TPs) by the enzymatic degradation at laboratory scale of two highly consumed antibiotics: tetracycline (Tc) and erythromycin (ERY). The analysis of the samples was carried out by a fast and simple method based on the novel configuration of the on-line turbulent flow system coupled to a hybrid linear ion trap – high resolution mass spectrometer. The method was optimized and validated for the complete analysis of ERY, Tc and their transformation products within 10 min without any other sample manipulation. Furthermore, the applicability of the on-line procedure was evaluated for 25 additional antibiotics, covering a wide range of chemical classes in different environmental waters with satisfactory quality parameters. Degradation rates obtained for Tc by laccase enzyme and ERY by EreB esterase enzyme without the presence of mediators were ∼78% and ∼50%, respectively. Concerning the identification of TPs, three suspected compounds for Tc and five of ERY have been proposed. In the case of Tc, the tentative molecular formulas with errors mass within 2 ppm have been based on the hypothesis of dehydroxylation, (bi)demethylation and oxidation of the rings A and C as major reactions. In contrast, the major TP detected for ERY has been identified as the “dehydration ERY-A”, with the same molecular formula of its parent compound. In addition, the evaluation of the antibiotic activity of the samples along the enzymatic treatments showed a decrease around 100% in both cases

Inequality across countries in energy intensities: an analysis of the role of energy transformation and final energy consumption

This paper analyzes the role of the energy transformation index and of final energy consumption per GDP unit in the disparities in energy intensity across countries. In that vein, we use a Theil decomposition approach to analyze global primary energy intensity inequality as well as inequality across different regions of the world and inequality within these regions. The paper first demonstrates the pre-eminence of divergence in final energy consumption per GDP unit in explaining global primary energy intensity inequality and its evolution during the 1971-2006 period. Secondly, it shows the lower (albeit non negligible) impact of the transformation index in global primary energy inequality. Thirdly, the relevance of regions as unit of analysis in studying crosscountry energy intensity inequality and their explanatory factors is highlighted. And finally, how regions around the world differ as to the relevance of the energy transformation index in explaining primary energy intensity inequality.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr)transformation to obtain the random vector y of dimension D. The factor model istheny = Λf + e (1)with the factors f of dimension k & D, the error term e, and the loadings matrix Λ.Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon a full-rank data matrix Y which is not the case for clr transformed data (see,e.g., Aitchison, 1986).The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Transformation rules form OntoProcED to OntoOKI

This file contains the transformtion rules in SWRL to translate formal specifications of two lower ontology levels (patterns and organization) to the upper level (implementation according to the OKI specification).

A type stars - physical parameters from UVBY and H-beta photometry

uvby H-beta photometry has been obtained for a sample of 93 selected main sequence A stars. The purpose was to determine accurate effective temperatures, surface gravities, and absolute magnitudes for an individual determination of ages and parallaxes, which have to be included in a more extensive work analyzing the kinematic properties of A V stars. Several calibrations and methods to determine the above mentioned parameters have been reviewed, allowing the design of a new algorithm for their determination. The results obtained using this procedure were tested in a previous paper using uvby H-beta data from the Hauck and Mermilliod catalogue, and comparing the rusulting temperatures, surface gravities and absolute magnitudes with empirical determinations of these parameters.

Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.