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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors used a class of U-statistics in various two-sample problems and extended the scope of applicability of the permutation tests to extend their applicability.
Abstract: SummaryThe two‐sample (as well as bhe single‐sample) perm utntion tests developed so far, are mostly based on linear permubation statistics. The object of the present invesbigation is to use a class of U‐statistics in various two‐sample problems and to extend the scope of applicability of the permutation tests.

9 citations

Book ChapterDOI
01 Jan 1999
TL;DR: A test for mutational linkage between two positions conditionally on the consensus pair is developed and illustrated with sequences from the V3 loop of the envelope gene from the human immunodeficiency virus.
Abstract: Some genomes mutate quickly. Studying their mutation process may allow us to understand the selection pressures these genomes are undergoing. Considering simultaneous mutations at several sites may provide insights into protein structure. We consider the situation where the frequency table for the aminoacid pairs can be summarized by a 2 ? 2 table. We develop a test for mutational linkage between two positions conditionally on the consensus pair. We illustrate the use of this test with sequences from the V3 loop of the envelope gene from the human immunodeficiency virus.

9 citations

Journal ArticleDOI
TL;DR: For probability densities not necessarily possessing finite Fisher information, an extended class of locally most powerful rank tests (LMPRT) is considered in this paper, and the existence of the asymptotic null distributions of all these LMPRT statistics is investigated.
Abstract: For probability densities not necessarily possessing finite Fisher information, an extended class of locally most powerful rank tests ‘LMPRT’ is considered. This class of LMPRT is partitioned into three disjoint subsets, characterized respectively by ‘i’ being asymptotically most powerful for «Pitman-type sequences of’ local ‘contiguous’ alternatives «AMPLA» and having asymptotically a normal null distribution ‘ANND» of the test statistic, ‘ii’ not necessarily being AMPLA, but having the ANND property, and ‘iii’ not necessarily being AMPLA and having asymptotically a non-normal null distribution of the test statistic. The current study focuses on the existence of the asymptotic null distributions of all these LMPRT statistics. In addition, an alternative distribution is suggested for inferences based on the LMPRT statistics of case ‘iii’

9 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider the problem of testing the validity of the cumulative distribution function assumption, and use parametric and non-parametric tests to compare the two sets of tolerainces.
Abstract: Apart from the possibility of measuring the exact amount, or dose, required to produce a specified response, the dilution (-direct) assay assumes that the cumulative distribution functions (cdf's) of the two different sets of tolerainces (to the standard and test preparations) have the same functional form, and differ onily by a constanit scale factor, which is, by definition, the relative potency. This paper considers the problem of testing the validity of this assumption, and useful parametric as well as non-parametric tests are discussed.

9 citations


Cited by
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Journal ArticleDOI
TL;DR: A nonparametric approach to the analysis of areas under correlated ROC curves is presented, by using the theory on generalized U-statistics to generate an estimated covariance matrix.
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.

16,496 citations

Journal Article
TL;DR: 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.
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

13,333 citations

Book
21 Mar 2002
TL;DR: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data is as discussed by the authors, 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.
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

9,509 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that a simple FDR controlling procedure for independent test statistics can also control the false discovery rate when test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses.
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.

9,335 citations

Journal ArticleDOI
TL;DR: In this article, a simple and robust estimator of regression coefficient β based on Kendall's rank correlation tau is studied, where the point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti.
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.

8,409 citations