Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

2000 Mathematics Subject Classification: 62G07, 60F10.

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Spatial distribution of schistosomiasis and geohelminthiasis cases in the rural areas of Pernambuco, Brazil

INTRODUCTION: The prevalence and intensity of geohelminth infections and schistosomiasis remain high in the rural areas of Zona da Mata, Pernambuco (ZMP), Brazil, where these parasites still represent a significant public health problem. The present study aimed to spatially assess the occurrences of schistosomiasis and geohelminthiasis in the ZMP. METHODS: The ZMP has a population of 1,132,544 inhabitants, formed by 43 municipalities. An ecological study was conducted, using secondary data relating to positive human cases and parasite loads of schistosomiasis and positive human cases of geohelminthiasis that were worked up in Excel 2007. We used the coordinates of the municipal headquarters to represent the cities which served as the unit of analysis of this study. The Kernel estimator was used to spatially analyze the data and identify distribution patterns and case densities, with analysis done in ArcGIS software. RESULTS: Spatial analysis from the Kernel intensity estimator made it possible to construct density maps showing that the northern ZMP was the region with the greatest number of children infected with parasites and the populations most intensely infected by Schistosoma mansoni. In relation to geohelminths, there was higher spatial distribution of cases of Ascaris lumbricoides and Trichuris trichiura in the southern ZMP, and greater occurrence of hookworms in the northern/central ZMP. CONCLUSIONS: Despite several surveys and studies showing occurrences of schistosomiasis and geohelminthiasis in the ZMP, no preventive measures that are known to have been effective in decreasing these health hazards have yet been implemented in the endemic area.

Aplicação da metodologia ROC na avaliação de desempenho de índices de gravidade clínica em unidades de neonatologia de Portugal

Tese de Doutoramento em Engenharia Industrial e de Sistemas

Análise da distribuição espaço-temporal de dengue e da infestação larvária no município de Tupã, Estado de São Paulo

INTRODUÇÃO: O vírus da dengue é transmitido pela picada do mosquito Aedes aegypti e, o atual programa de controle não atinge o objetivo de impedir sua transmissão. Este trabalho objetivou analisar a relação entre a distribuição espaço-temporal de casos de dengue e os indicadores larvários no município de Tupã, de janeiro de 2004 a dezembro de 2007. MÉTODOS: Foram construídos indicadores larvários por quarteirão e totalidade do município. Utilizou-se o método cross-lagged correlation para avaliar a correlação entre casos de dengue e indicadores larvários. Foi utilizado estimador kernel para análise espacial. RESULTADOS: A correlação cruzada defasada entre casos de dengue e indicadores larvários foi significativa. Os mapas do estimador Kernel da positividade de recipientes indicam uma distribuição heterogênea, ao longo do período estudado. Nos dois anos de transmissão, a epidemia ocorreu em diferentes regiões. CONCLUSÕES: Não ficou evidenciada relação espacial entre infestação larvária e ocorrência de dengue. A incorporação de técnicas de geoprocessamento e análise espacial no programa, desde que utilizados imediatamente após a realização das atividades, podem contribuir com as ações de controle, indicando os aglomerados espaciais de maior incidência.

Estimadores do tipo núcleo para Variávei s I.I.D. com espaço de estados geral

In this work, the paper of Campos and Dorea [3] was detailed. In that article a Kernel Estimator was applied to a sequence of random variables with general state space, which were independent and identicaly distributed. In chapter 2, the estimator´s properties such as asymptotic unbiasedness, consistency in quadratic mean, strong consistency and asymptotic normality were verified. In chapter 3, using R software, numerical experiments were developed in order to give a visual idea of the estimate process

Análise de técnicas de distribuição espacial com padrões pontuais e aplicação a dados de acidentes de trânsito e a dados da dengue de Rio Claro-SP

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Queima de biomassa na região amazônica e seus efeitos sobre a saúde: uma abordagem espacial

Pós-graduação em Engenharia Mecânica - FEG

Geoprocessamento aplicado à dengue.descrição espaço-temporal das epidemias ocorridas no município de cruzeiro/sp nos anos de 2006 e 2011

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Space-time description of dengue epidemic in Cruzeiro, SP, in 2006 and 2011

Objective: to identify patterns in the spatial and temporal distribution of cases of dengue fever occurring in the city of Cruzeiro, state of Sao Paulo (SP).Methods: an ecological and exploratory study was undertaken using spatial analysis tools and data from dengue cases obtained on the SinanNet. The analysis was carried out by area, using the IBGE census sector as a unit. The months of March to June 2006 and 2011 were assessed, revealing progress of the disease. TerraView 3.3.1 was used to calculate the Global Moran's I, month to month, and the Kernel estimator.Results: in the year 2006, 691 cases of dengue fever (rate of 864.2 cases/100,000 inhabitants) were georeferenced; and the Moran's I and p-values were significant in the months of April and May (TM = 0.28; p = 0.01; I-M = 0.20; p = 0.01) with higher densities in the central, north, northeast and south regions. In the year 2011, 654 cases of dengue fever (rate of 886.8 cases/100,000 inhabitants) were georeferenced; and the Moran's I and p-values were significant in the months of April and May (I, = 0.28; p = 0.01; I-M = 0.16; p = 0.05) with densities in the same regions as 2006. The Global Moran's I is a global measure of spatial autocorrelation, which indicates the degree of spatial association in the set of information from the product in relation to the average. The I varies between -1 and +1 and can be attributed to a level of significance (p-value). The positive value points to a positive or direct spatial autocorrelation.Conclusion: we were able to identify patterns in the spatial and temporal distribution of dengue cases occurring in the city of Cruzeiro, SP, and locate the census sectors where the outbreak began and how it evolved.

Admissions due to pneumonia and biomass burning: a spatial approach

Objective: To identify spatial patterns in rates of admission for pneumonia among children and relate them to the number of fires reported in the state of Mato Grosso, Brazil. Methods: We conducted an ecological and exploratory study of data from the state of Mato Grosso for 2008 and 2009 on hospital admissions of children aged 0 to 4 years due to pneumonia and on fires in the same period. Admission rates were calculated and choropleth maps were plotted for rates and for fire outbreaks, Moran's I was calculated and the kernel estimator used to identify "hotspots." Data were analyzed using TerraView 3.3.1. Results: Fifteen thousand six hundred eighty-nine children were hospitalized (range zero to 2,315), and there were 161,785 fires (range 7 to 6,454). The average rate of admissions per 1,000 inhabitants was 2.89 (standard deviation [SD] = 5.18) and the number of fires per 1,000 inhabitants was 152.81 (SD = 199.91). Moran's I for the overall number of admissions was I = 0.02 (p = 0.26), the index for rate of admission was I = 0.02 (p = 0.21) and the index for the number of fires was I = 0.31 (p < 0.01). It proved possible to identify four municipalities with elevated rates of admissions for pneumonia. It was also possible to identify two regions with high admission densities. A clustering of fires was evident along what is known as the "arc of deforestation." Conclusions: This study identified municipalities in the state of Mato Grosso that require interventions to reduce rates of admission due to pneumonia and the number fires.

Smooth Estimation of a Monotone Density

We investigate the interplay of smoothness and monotonicity assumptions when estimating a density from a sample of observations. The nonparametric maximum likelihood estimator of a decreasing density on the positive half line attains a rate of convergence at a fixed point if the density has a negative derivative. The same rate is obtained by a kernel estimator, but the limit distributions are different. If the density is both differentiable and known to be monotone, then a third estimator is obtained by isotonization of a kernel estimator. We show that this again attains the rate of convergence and compare the limit distributors of the three types of estimators. It is shown that both isotonization and smoothing lead to a more concentrated limit distribution and we study the dependence on the proportionality constant in the bandwidth. We also show that isotonization does not change the limit behavior of a kernel estimator with a larger bandwidth, in the case that the density is known to have more than one derivative.

DECOMPOSITION OF REGRESSION ESTIMATORS TO EXPLORE THE INFLUENCE OF "UNMEASURED" TIME-VARYING CONFOUNDERS

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth function of time, St, using a kernel estimator is roughly equivalent to estimating the association with a linear combination of the b(u)s with weights that involve two components: the assumptions about the smoothness of St and the normalized variogram of the X process. When an unmeasured confounder U exists, but the model otherwise correctly controls for measured confounders, the excess variation in b(u)s is evidence of confounding by U. We use the plot of b(u)s versus lag u, lagged-estimator-plot (LEP), to diagnose the influence of U on the effect of X on Y. We use appropriate linear combination of b(u)s or extrapolate to b(0) to obtain novel estimators that are more robust to the influence of smooth U. The methods are extended to time series log-linear models and to spatial analyses. The LEP plot gives us a direct view of the magnitude of the estimators for each lag u and provides evidence when models did not adequately describe the data.