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.

Some aspects of the statistical analysis of the 'mixed model'.

Abstract: This paper deals with the statistical analysis (both parametric and non-parametric) of 'mixed model' experiments. The general structure of such experiments involves n randomly chosen subjects who respond once to each of p distinct treatments. Thus the subject or block effects are random and treatment effects are fixed. The hypothesis of no treatment effects is considered under several different combinations of assumptions concerning the joint distribution of the observations corresponding to each of the particular subjects. For each situation, an appropriate test procedure is discussed and its properties studied. The different methods considered in the paper are illustrated in detail in two numerical examples. These examples have been chosen to illustrate the relative performances of the different test criteria for a situation in which the null hypothesis is essentially true (Example 1) and for a situation in which the null hypothesis is essentially false (Example 2). The reader may wish to begin by studying these examples for a better understanding of the theory. Finally, the section on examples contains algorithms for the efficient computation of the various test criteria. A computer program based on these algorithms has been written and can be made available to any interested persons.

Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes

Abstract: For a stationary $\phi$-mixing sequence of stochastic $p(\geqq 1)$-vectors, weak convergence of the empirical process (in the $J_1$-topology on $D^p\lbrack 0, 1 \rbrack)$ to an appropriate Gaussian process is established under a simple condition on the mixing constants $\{\phi_n\}$. Weak convergence for random number of stochastic vectors is also studied. Tail probability inequalities for Kolmogorov Smirnov statistics are provided.

Estimating correlation by using a general linear mixed model: evaluation of the relationship between the concentration of HIV-1 RNA in blood and semen.

Abstract: Estimating the correlation coefficient between two outcome variables is one of the most important aspects of epidemiological and clinical research. A simple Pearson's correlation coefficient method is usually employed when there are complete independent data points for both outcome variables. However, researchers often deal with correlated observations in a longitudinal setting with missing values where a simple Pearson's correlation coefficient method cannot be used. General linear mixed models (GLMM) techniques were used to estimate correlation coefficients in a longitudinal data set with missing values. A random regression mixed model with unstructured covariance matrix was employed to estimate correlation coefficients between concentrations of HIV-1 RNA in blood and seminal plasma. The effects of CD4 count and antiretroviral therapy were also examined. We used data sets from three different centres (650 samples from 238 patients) where blood and seminal plasma HIV-1 RNA concentrations were collected from patients; 137 samples from 90 different patients without antiviral therapy and 513 samples from 148 patients receiving therapy were considered for analysis. We found no significant correlation between blood and semen HIV-1 RNA concentration in the absence of antiviral therapy. However, a moderate correlation between blood and semen HIV-1 RNA was observed among subjects with lower CD4 counts receiving therapy. Our findings confirm and extend the idea that the concentrations of HIV-1 in semen often differ from the HIV-1 concentration in blood. Antiretroviral therapy administered to subjects with low CD4 counts result in sufficient concomitant reduction of HIV-1 in blood and semen so as to improve the correlation between these compartments. These results have important implications for studies related to the sexual transmission of HIV, and development of HIV prevention strategies.

From Finite Sample to Asymptotic Methods in Statistics

Abstract: Exact statistical inference may be employed in diverse fields of science and technology. As problems become more complex and sample sizes become larger, mathematical and computational difficulties can arise that require the use of approximate statistical methods. Such methods are justified by asymptotic arguments but are still based on the concepts and principles that underlie exact statistical inference. With this in perspective, this book presents a broad view of exact statistical inference and the development of asymptotic statistical inference, providing a justification for the use of asymptotic methods for large samples. Methodological results are developed on a concrete and yet rigorous mathematical level and are applied to a variety of problems that include categorical data, regression, and survival analyses. This book is designed as a textbook for advanced undergraduate or beginning graduate students in statistics, biostatistics, or applied statistics but may also be used as a reference for academic researchers.

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.