Showing papers by "Pranab Kumar Sen published in 2012"

Methodology in Robust and Nonparametric Statistics

Abstract: Introduction and Synopsis Introduction Synopsis Preliminaries Introduction Inference in Linear Models Robustness Concepts Robust and Minimax Estimation of Location Clippings from Probability and Asymptotic Theory Problems Robust Estimation of Location and Regression Introduction M-Estimators L-Estimators R-Estimators Minimum Distance and Pitman Estimators Differentiable Statistical Functions Problems Asymptotic Representations for L-Estimators Introduction Bahadur Representations for Sample Quantiles L-Statistics with Smooth Scores General L-Estimators Statistical Functionals Second-Order Asymptotic Distributional Representations L-Estimation in Linear Model Breakdown Point of L- and M-Estimators Further Developments Problems Asymptotic Representations for M-Estimators Introduction M-Estimation of General Parameters M-Estimation of Location: Fixed Scale Studentized M-Estimators of Location M-Estimation in Linear Model Studentizing Scale Statistics Hadamard Differentiability in Linear Models Further Developments Problems Asymptotic Representations for R-Estimators Introduction Asymptotic Representations for R-Estimators of Location Representations for R-Estimators in Linear Model Regression Rank Scores Inference Based on Regression Rank Scores Bibliographical Notes Problems Asymptotic Interrelations of Estimators Introduction Estimators of location Estimation in linear model Approximation by One-Step Versions Further developments Problems Robust Estimation: Multivariate Perspectives Introduction The Notion of Multivariate Symmetry Multivariate Location Estimation Multivariate Regression Estimation Affine-Equivariant Robust Estimation Efficiency and Minimum Risk Estimation Stein-Rule Estimators and Minimum Risk Efficiency Robust Estimation of Multivariate Scatter Some Complementary and Supplementary Notes Problems Robust Tests and Confidence Sets Introduction M-Tests and R-Tests Minimax Tests Robust Confidence Sets Multiparameter Confidence Sets Affine-Equivariant Tests and Confidence Sets Problems Robust Estimation: Multivariate Perspectives Introduction The Notion of Multivariate Symmetry Multivariate Location Estimation Multivariate Regression Estimation Affine-Equivariant Robust Estimation Efficiency and Minimum Risk Estimation Stein-Rule Estimators and Minimum Risk Efficiency Robust Estimation of Multivariate Scatter Some Complementary and Supplementary Notes Problems Robust Tests and Confidence Sets Introduction M-Tests and R-Tests Minimax Tests Robust Confidence Sets Multiparameter Confidence Sets Affine-Equivariant Tests and Confidence Sets Problems

Robust permutation tests for homogeneity of fingerprint patterns of dioxin congener profiles

Abstract: Fingerprint analysis comparing the polychlorinated dibenzo-p-dioxin and dibenzofuran (PCDD/F) congener profile patterns of collected samples with those of potential dioxin emission source(s) is an important tool for identifying environmental dioxin pollution. The constraint that the proportions of the 17 PCDD/F congeners comprising a fingerprint sum up to one motivates a multivariate gamma distribution, which leads to a Dirichlet distribution. Because of the complexity in restricted likelihood ratio tests and typical sample size limitations resulting from laboratory analysis costs, permutation test procedures are employed for hypothesis testing of the homogeneity of congener profiles. Pearson-type chi-squared tests based on the Dirichlet distribution (DM) assumption, the generalized form of DM using the arithmetic mean and geometric mean of the proportions, and the robust aligned rank test, are proposed and compared through simulations. PCDD/F samples collected from the stack of a local municipal solid waste incinerator and from ambient air near the municipal solid waste incinerator in Taiwan were illustrated as an example. The simulation results showed that the aligned rank test, followed by the DM-based test, was generally robust to distributional assumptions and had high statistical power. The arithmetic-mean-based and geometric-mean-based tests outperformed one another in different conditions, dependent on the underlying distribution. Copyright © 2012 John Wiley & Sons, Ltd.

The Use of Hamming Distance in Bioinformatics

Abstract: We present the major issues concerning the use of the Hamming distance and its generalizations in bioinformatics. Hamming distance type measures have enjoyed a perennial usage in the fields of biodiversity, genetics, ecology, among many others. Bioinformatics data bring new challenges to statistical procedures. Dependence among variates is presented in stochastic as well as functional forms. The classical asymptotic paradigm of very large data sets formed by a small number of variates is usually inappropriate in bioinformatics data, in which usually one expects a few observations each of very high dimension. Thus, parametric modeling may be unsuitable in many situations in bioinformatics and its shortcomings may appear hidden as spurious statistical artifacts. The Hamming distance, in its classical or modified versions, is a very powerful tool for the statistical analysis of such data. Its functional straightforwardness results in fast calculations even for very large data sets, and interpretations are easily obtained. Moreover, we can successfully employ Hamming distance based test statistics for studies concerning population heterogeneity. These statistics belong to a large class called quasi U-statistics for which desirable asymptotic properties are attainable under mild regularity conditions. The use of generalized Hamming distance is exemplified by a real DNA data set.

Quality of Life Perspectives in Chronic Disease and Disorder Studies

Abstract: For diabetes and some other chronic diseases or disorders usually some nondegradation stochastic processes are encountered in quality of life (QoL) studies These processes may not exhibit the degradation phenomenon until some other complications arise, as illustrated with two notable examples The biology of these disorders is outlined and along with the formulation of degradation and nondegradation stochastic processes, QoL perspectives are emphasized The concept of adjusted quality-adjusted survival analysis underlies our discussion A small simulation study is also appended

Introduction: Wither Bioinformatics in Human Health and Heredity

Abstract: With a working definition of bioinformatics provided, this chapter briefly outlines the premises with which integration of information from several disciplines are used in this newly introduced discipline. While not an entirely new subject, research areas of bioinformatics have wide diversity and they have important implications not only in basic science, particularly in molecular biology, systems biology, and genomics, but also in translational research with applications in medical, public health, and health policy practices. We note that bioinformatics and computational biology are not synonymous, but they adhere to a common broader interdisciplinary field. With illustrations of different research areas within this subject, some of which are addressed in the chapters of this volume, this introduction ends with a listing of some of the open areas of research in bioinformatics.