On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

2000 Mathematics Subject Classification: 62G07, 62L20.

Classical horizontal inequity and reranking: an integrated approach

The last 20 years have seen a significant evolution in the literature on horizontal inequity (HI) and have generated two major and "rival" methodological strands, namely, classical HI and reranking. We propose in this paper a class of ethically flexible tools that integrate these two strands. This is achieved using a measure of inequality that merges the well-known Gini coefficient and Atkinson indices, and that allows a decomposition of the total redistributive effect of taxes and transfers in a vertical equity effect and a loss of redistribution due to either classical HI or reranking. An inequality-change approach and a money-metric cost-of-inequality approach are developed. The latter approach makes aggregate classical HI decomposable across groups. As in recent work, equals are identified through a nonparametric estimation of the joint density of gross and net incomes. An illustration using Canadian data from 1981 to 1994 shows a substantial, and increasing, robust erosion of redistribution attributable both to classical HI and to reranking, but does not reveal which of reranking or classical HI is more important since this requires a judgement that is fundamentally normative in nature.

Sur les prolongements de sous-copules

L’objet du travail est d’étudier les prolongements de sous-copules. Un cas important de l’utilisation de tels prolongements est l’estimation non paramétrique d’une copule par le lissage d’une sous-copule (la copule empirique). Lorsque l’estimateur obtenu est une copule, cet estimateur est un prolongement de la souscopule. La thèse présente au chapitre 2 la construction et la convergence uniforme d’un estimateur bona fide d’une copule ou d’une densité de copule. Cet estimateur est un prolongement de type copule empirique basé sur le lissage par le produit tensoriel de fonctions de répartition splines. Le chapitre 3 donne la caractérisation de l’ensemble des prolongements possibles d’une sous-copule. Ce sujet a été traité par le passé; mais les constructions proposées ne s’appliquent pas à la dépendance dans des espaces très généraux. Le chapitre 4 s’attèle à résoudre le problème suivant posé par [Carley, 2002]. Il s’agit de trouver la borne supérieure des prolongements en dimension 3 d’une sous-copule de domaine fini.

Statistical Inference for Some Measures of System Availability

Department of Statistics, Cochin University of Science and Technology

Measuring and testing for the systemically important financial institutions

This paper analyzes the measure of systemic importance ∆CoV aR proposed by Adrian and Brunnermeier (2009, 2010) within the context of a similar class of risk measures used in the risk management literature. In addition, we develop a series of testing procedures, based on ∆CoV aR, to identify and rank the systemically important institutions. We stress the importance of statistical testing in interpreting the measure of systemic importance. An empirical application illustrates the testing procedures, using equity data for three European banks.

Efficient modeling and inference for event-related fMRI data

Event-related functional magnetic resonance imaging (efMRI) has emerged as a powerful technique for detecting brains' responses to presented stimuli. A primary goal in efMRI data analysis is to estimate the Hemodynamic Response Function (HRF) and to locate activated regions in human brains when specific tasks are performed. This paper develops new methodologies that are important improvements not only to parametric but also to nonparametric estimation and hypothesis testing of the HRF. First, an effective and computationally fast scheme for estimating the error covariance matrix for efMRI is proposed. Second, methodologies for estimation and hypothesis testing of the HRF are developed. Simulations support the effectiveness of our proposed methods. When applied to an efMRI dataset from an emotional control study, our method reveals more meaningful findings than the popular methods offered by AFNI and FSL. (C) 2008 Elsevier B.V. All rights reserved.

Condicionantes socioeconômicos e ambientais dos clubes de convergência da renda na Amazônia Legal 1985 a 2007

Este trabalho analisa a formação de clubes de convergência na Amazônia legal no período de 1985 a 2007, condicionados por variáveis socioeconômicas, institucionais e ambientais. O caráter inovador deste trabalho está em testar pela primeira vez a importância do desmatamento como condicionante ambiental da formação dos clubes de convergência na Amazônia. Foi utilizada uma metodologia não paramétrica através da estimação de densidades de núcleo, matriz de transição e estimação de núcleos estocásticos para testar as evidências de convergência entre os municípios. Os resultados confirmaram a hipótese de convergência, grande dinâmica intrasseccional da renda e a formação de três clubes de convergência entre os municípios da Amazônia legal. O capital humano aparece como importante condicionante e o rebanho bovino e área de pecuária tem fraca significância no condicionamento da renda relativa municipal. O desmatamento e as variáveis institucionais não se mostraram significantes para o crescimento econômico dos municípios da Amazônia legal.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Consistency of Concave Regression with an Application to Current-Status Data

We consider the problem of nonparametric estimation of a concave regression function F. We show that the supremum distance between the least square s estimatorand F on a compact interval is typically of order(log(n)/n)2/5. This entails rates of convergence for the estimator’s derivative. Moreover, we discuss the impact of additional constraints on F such as monotonicity and pointwise bounds. Then we apply these results to the analysis of current status data, where the distribution function of the event times is assumed to be concave.

Venous thromboembolism in patients with acute leukemia: Prevalence, incidence, recurrence of thrombosis, risk factors, and impact on survival

Venous thromboembolism (VTE), including deep vein thrombosis (DVT) and pulmonary embolism (PE), is the third most preventable cardiovascular disease and a growing public health problem in the United States. The incidence of VTE remains high with an annual estimate of more than 600,000 symptomatic events. DVT affects an estimated 2 million American each year with a death toll of 300,000 persons per year from DVT-related PE. Leukemia patients are at high risk for both hemorrhage and thrombosis; however, little is known about thrombosis among acute leukemia patients. The ultimate goal of this dissertation was to obtain deep understanding of thrombotic issue among acute leukemia patients. The dissertation was presented in a format of three papers. First paper mainly looked at distribution and risk factors associated with development of VTE among patients with acute leukemia prior to leukemia treatment. Second paper looked at incidence, risk factors, and impact of VTE on survival of patients with acute lymphoblastic leukemia during treatment. Third paper looked at recurrence and risk factors for VTE recurrence among acute leukemia patients with an initial episode of VTE. Descriptive statistics, Chi-squared or Fisher's exact test, median test, Mann-Whitney test, logistic regression analysis, Nonparametric Estimation Kaplan-Meier with a log-rank test or Cox model were used when appropriate. Results from analyses indicated that acute leukemia patients had a high prevalence, incidence, and recurrent rate of VTE. Prior history of VTE, obesity, older age, low platelet account, presence of Philadelphia positive ALL, use of oral contraceptives or hormone replacement therapy, presence of malignancies, and co-morbidities may place leukemia patients at an increased risk for VTE development or recurrence. Interestingly, development of VTE was not associated with a higher risk of death among hospitalized acute leukemia patients.^

Estimation of nonparametric probability density functions with applications to automatic speech recognition

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2007

Estimation of dynamic latent variable models using simulated nonparametric moments

Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Since conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. Monte Carlo results show that the estimator performs well in comparison to other estimators that have been proposed for estimation of general DLV models.

Estimation of dynamic latent variable models using simulated nonparametric moments

Abstract. Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Because conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. It is shown that as the number of simulations diverges, the estimator is consistent and a higher-order expansion reveals the stochastic difference between the infeasible GMM estimator based on the same moment conditions and the simulated version. In particular, we show how to adjust standard errors to account for the simulations. Monte Carlo results show how the estimator may be applied to a range of dynamic latent variable (DLV) models, and that it performs well in comparison to several other estimators that have been proposed for DLV models.

Estimation of parametric and nonparametric models for univariate claim severity distributions - an approach using R

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described