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.

Tests of homogeneity of intercepts after a preliminary test

Abstract: For the multl-sample regression model , the problem of testing equality of intercepts following a preliminarytest on the equality o f slopes is considered. The t e s t s are based on the conventional least squares estimators (without necessarily assuming the normality of the underlying error distributions ) , and the impact of a preliminary test on the asymptotic size and power of the final test is studied.

1 Bioenvironment and public health: Statistical perspectives

Abstract: At this concluding phase of the present century (and the millennium too), the limelight of advancement of knowledge has been stolen primarily by the spectacular advent of information technology (IT). Modern electronics and computers have invaded each and every corne'" of the globe, and touched all walks of life, science and technolgy, and society. And yet, ma jor challanges have errupted from almost every sphere of life on earth, most noticably, in the sectors of bioenvironment and public health. Our bioenvironment constitutes the totality of entities of all socio-economic, cultutal-political, clinical and biomedical, ecological and environmental, as well as environmental health and hazard perspectives that pertain to the existence and propagation of all biosystems on earth, including, of course, the human beings. Public awareness of such bioenvironmental impacts on human health and quality of life (QOL) has been an important ingredient in the constitution and development of the public health science and practice field, and together, these two broad disciplines form a broader interdisciplinary field that deserves our utmost attention from scientific as well as humanitarian perspectives. No longer, the field of public health is specifically confined to the disease prevention and health promotion aspects of human beings, and bioenvironment has emerged as one of the most influencing factors in public health, and only taken together, they convey a much more comprehensive picture. The eco-environment of our mother planet is indeed endangered with life-threatening phenomena, not only due to escalating ecological imbalances and environmental disasters, but also due to mounting social, economic, religious, political and cultural disruptions; relatively new or hitherto unknown forms of catastrophic diseases or disorders (such as the HIV) have drastically altered the QOL of all biosystems on earth, and bioenvironmental toxicity of various kinds has attained an elevated level that poses a serious threat to the

The Generalized Pair Chart for Right­Censored Observations

Abstract: The pair chart is known to be a convenient descriptive tool in comparing two samples and in calculating and interpreting various nonparametric procedures for the two­sample problem (see Quade (1973)). To incorporate rightcensored data in the two­sample problem, a generalized pair chart is considered and the same is utilized in the schematic computation of Gehan's W­statistic (Gehan (1965)) and a triplet statistic (see Crouse and Steffens (1969)) among others. An alternative pair chart based on partial observations is also considered. A maximal distance statistic, based on the generalized pair chart, has been considered for testing the hypothesis of equality of the two distributions.

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.