Pranab Kumar Sen

Bio: Pranab Kumar Sen is an academic researcher from University of North Carolina at Chapel Hill. The author has contributed to research in topics: Estimator & Nonparametric statistics. The author has an hindex of 51, co-authored 570 publications receiving 19997 citations. Previous affiliations of Pranab Kumar Sen include Indian Statistical Institute & Academia Sinica.

Asymptotic Comparison Of A Class Of Multivariate Multiparameter Tests

Abstract: In the context of growth curve models and elsewhere, one is faced with the problem of studying the relative performances of two (or more) tests of significance for some multiparameter hypotheses where the associated test statistics have (limiting) chi-square distributions (central under the null and noncentral under alternative hypotheses) , with possible different degrees of freedom. Since the standard Pitman-efficiency does not work ¦ out well in such a case, three alternative criteria of asymptotic relative efficiency are developed here, and their properties studied. It is noted that the efficiencies for each of the three criteria are products of a scalar adjustment function and a term involving the noncentrality parameters. Values of the scalar adjustment factor are included for selected values of the degrees of freedom and the size of the tests.

Bioenvironmental and public health statistics

Abstract: One aspect of statistical methodology that merits special appraisal is the extent of the appropriateness of standard tools in non-standard applications. This volume adopts an unorthodox approach to ensure relevant biostatistical methods are considered in the context of fruitful applications.

Change Point Problem Relating to the Poverty Structure

Abstract: An index of poverty reflects the extent to which individuals in a society or community fall below a minimal acceptable standard of living. It is generally framed in terms of a set poverty line, the income distribution of the poor, and other social welfare functions relevant to the poverty structure; the Gini coefficient plays a vital role in this context. The income distribution and other measures based on this distribution rarely remain stationary over time, so that in studying the poverty structure over a period of time, one essentially encounters a time-dependent model that may be analyzed in a parametric or nonparametric manner. In this context, the change point problem is very relevant, and the related methodology is considered in a systematic manner.

Preliminary Test Isotonic M-Estimation in Some Multivariate Linear Models

Abstract: For the usual multivariate linear model, preliminary test Mestimation theory is considered in an isotonic setup. Roy's union-intersection principle is incorporated in a formulation of suitable isotonic M-procedures for the preliminary testing component, following which M-estimator of location are presented in the same vein. The main thrust is on the development of the related asymptotic theory with a view to studying the allied robustness aspects. A numerical illustration is set to demonstrate the superiority of the proposed approach.

Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach.

Abstract: Methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed. When a test is based on an observed variable that lies on a continuous or graded scale, an assessment of the overall value of the test can be made through the use of a receiver operating characteristic (ROC) curve. The curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates. When two or more empirical curves are constructed based on tests performed on the same individuals, statistical analysis on differences between curves must take into account the correlated nature of the data. This paper presents a nonparametric approach to the analysis of areas under correlated ROC curves, by using the theory on generalized U-statistics to generate an estimated covariance matrix.

The Design and Analysis of Experiments

Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

Experimental Design and Data Analysis for Biologists

Abstract: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

The control of the false discovery rate in multiple testing under dependency

Abstract: Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate. We prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses. This condition for positive dependency is general enough to cover many problems of practical interest, including the comparisons of many treatments with a single control, multivariate normal test statistics with positive correlation matrix and multivariate $t$. Furthermore, the test statistics may be discrete, and the tested hypotheses composite without posing special difficulties. For all other forms of dependency, a simple conservative modification of the procedure controls the false discovery rate. Thus the range of problems for which a procedure with proven FDR control can be offered is greatly increased.

Estimates of the Regression Coefficient Based on Kendall's Tau

Abstract: The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti , and is unbiased. The confidence interval is also determined by two order statistics of this set of slopes. Various properties of these estimators are studied and compared with those of the least squares and some other nonparametric estimators.