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 Properties of Maximum Likelihood Estimators Based on Conditional Specification

Abstract: Along with the asymptotic distribution, expressions for the asymptotic bias and asymptotic dispersion matrix of the preliminary test maximum likelihood estimator for a general multi-sample parametric model (when the null hypothesis relating to the restraints on the parameters may not hold) are derived and compared with the parallel expressions for the unrestricted and restricted maximum likelihood estimators. This study reveals the robustness property of the preliminary test estimator when the assumed restraints may not hold.

Pitman's Measure of Closeness: A Comparison of Statistical Estimators

Abstract: Preface Part I. Introduction 1. Evolution of Estimation Theory Least Squares Method of Moments Maximum Likelihood Uniformly Minimum Variance Unbiased Estimation Biased Estimation Bayes and Empirical Bayes Influence Functions and Resampling Techniques Future Directions 2. PMC Comes of Age PMC: A Product of Controversy PMC as an Intuitive Criterion 3. The Scope of the Book History, Motivation, and Controversy of PMC A Unified Development of PMC Part II. Development of Pitman's Measure of Closeness: 1. The Intrinsic Appeal of PMC Use of MSE Historical Development of PMC Convenience Store Example 2. The Concept of Risk Renyi's Decomposition of Risk How Do We Understand Risk? 3. Weakness in the Use of Risk When MSE Does Not Exist Sensitivity to the Choice of the Loss Function The Golden Standard 4. Joint Versus Marginal Information Comparing Estimators with an Absolute Ideal Comparing Estimators with One Another 5. Concordance of PMC with MSE and MAD Part III. Anomalies with PMC: 1. Living in an Intransitive World Round-Robin Competition Voting Preferences Transitiveness 2. Paradoxes Among Choice The Pairwise-Worst Simultaneous-Best Paradox The Pairwise-Best Simultaneous-Worst Paradox Politics: The Choice of Extremes 3. Rao's Phenomenom 4. The Question of Ties Equal Probability of Ties Correcting the Pitman Criterion A Randomized Estimator 5. The Rao-Berkson Controversy Minimum Chi-Square and Maximum Likelihood Model Inconsistency Remarks Part 4. Pairwise Comparisons 1. Geary-Rao Theorem 2. Applications of the Geary-Rao Theorem 3. Karlin's Corollary 4. A Special Case of the Geary-Rao Theorem Surjective Estimators The MLR Property 5. Applications of the Special Case 6. Transitiveness Transitiveness Theorem Another Extension of Karlin's Corollary Part V. Pitman-Closest Estimators: 1. Estimation of Location Parameters 2. Estimators of Scale 3. Generalization via Topological Groups 4. Posterior Pitman Closeness 5. Linear Combinations 6. Estimation by Order Statistics Part 6. Asymptotics and PMC 1. Pitman Closeness of BAN Estimators Modes of Convergence Fisher Information BAN Estimates are Pitman Closet 2. PMC by Asymptotic Representations A General Proposition 3. Robust Estimation of a Location Parameter L-Estimators M-Estimators R-Estimators 4. APC Characterizations of Other Estimators Pitman Estimators Examples of Pitman Estimators PMC Equivalence Bayes Estimators 5. Second-Order Efficiency and PMC Asymptotic Efficiencies Asymptotic Median Unbiasedness Higher-Order PMC Index Bibliography.

Asymptotic Normality of Sample Quantiles for $m$-Dependent Processes

Abstract: The usual technique of deriving the asymptotic normality of a quantile of a sample in which the random variables are all independent and identically distributed [cf. Cramer (1946), pp. 367-369] fails to provide the same result for an $m$-dependent (and possibly non-stationary) process, where the successive observations are not independent and the (marginal) distributions are not necessarily all identical. For this reason, the derivation of the asymptotic normality is approached here indirectly. It is shown that under certain mild restrictions, the asymptotic almost sure equivalence of the standardized forms of a sample quantile and the empirical distribution function at the corresponding population quantile, studied by Bahadur (1966) [see also Kiefer (1967)] for a stationary independent process, extends to an $m$-dependent process, not necessarily stationary. Conclusions about the asymptotic normality of sample quantiles then follow by utilizing this equivalence in conjunction with the asymptotic normality of the empirical distribution function under suitable restrictions. For this purpose, the results of Hoeffding (1963) and Hoeffding and Robbins (1948) are extensively used. Useful applications of the derived results are also indicated.

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.