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.

Invariance principles for jackknifing U-statistics for finite population sampling and some applications

Abstract: For simple random sampling (without replacement) from a finite population, suitable stochastic processes are constructed from the entire sequence of jackknife estimators based on smooth functions of U-statistics and these are approximated (in distributions) by some Brownian bridge processes. Strong convergence of the Tukey estimator of the variance of a jackknife U-statistic has been interpreted suitably and established. Some applications of these results in sequential analysis relating to finite population sampling are also considered.

A Generalization of the T-Method of Multiple Comparisons for Interactions

Abstract: Tukey's [4] T-(maximum modulus) method of multiple comparisons is applicable to homoscedastic and equally correlated normally distributed random variables. For multiple comparisons on interaction effects (in factorial experiments), the allied random variables are not equally correlated. Nevertheless, it is shown that the T-method holds in this situation. The theory is illustrated by an example on a partially balanced incomplete block (PBIB) design.

1 Randomization procedures

Abstract: Publisher Summary This chapter describes the randomization procedures. Randomization procedures are the precursors of the nonparametric ones, and, during the past fifty years, they have played a fundamental role in the evolution of distribution-free methods. Traditional developments on randomization procedures (mostly, in the thirties) were spotty and piecemeal. Randomization procedures are also developed for drawing statistical inference from some stochastic processes and some non-standard problems too. Characterization of various nonparametric hypotheses in terms of invariance (of the (joint) distribution of the sample point) under certain (finite) groups of transformations (which map the sample space onto itself) led to the constitution of maximal invariants that play the key role in the construction of randomization tests. Randomization procedures allow easy adjustments for ties or some other irregularities which may be encountered in practical applications. The chapter also provides a basic survey of the randomization procedures in the wide spectrum of applications.

Weak convergence of a weighted residual empirical process in autoregression

Abstract: This paper proves the weak convergence of certain randomly weighted residual empirical processes in the first order autoregression model to a continuous Gaussian process. The result is used to derive the asymptotic uniform linearity of the given processes and of certain class of linear rank statistics based on the residuals in the estimated parameters. These latter results are used to study the asymptotic behavior of certain goodness-offit tests and R-estimators of the autoregression parameter. AMS 1980 subject classifications: Primary 60 Β 10, secondary 62 E 20, 62 M 10

Spearman's footrule under progressive censoring

Abstract: Spearman's footrule, a well-known measure of rank correlation, is extended here to progressively censored rankings. Under the hypothesis of randomness ( i.e. , under random ranking), a martingale characterization is exploited in the formulation of a functional central limit theorem, and its applications in incomplete rankings are illustrated.

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.