Showing papers by "Pranab Kumar Sen published in 1993"

Large Sample Methods in Statistics: An Introduction With Applications

Abstract: This text bridges the gap between sound theoretcial developments and practical, fruitful methodology by providing solid justification for standard symptotic statistical methods. It contains a unified survey of standard large sample theory and provides access to more complex statistical models that arise in diverse practical applications.

Stochastic processes : a Festschrift in honour of Gopinath Kallianpur

Abstract: This volume celebrates the many contributions which "Gopinath Kallianpur" has made to probability and statistics. It comprises 40 chapters which taken together survey the wide sweep of ideas which have been influenced by Professor Kallianpur's writing and research. All the chapters have been written by experts in their respective fields and as a result the volume provides a comprehensive survey of the current state of research in stochastic processes.

Replicated piecewise stopping numbers and sequential analysis

Abstract: For certain basic problems in sequential analysis,it is shown that a piecewise sequential methodology resting on replicated piecewise stopping numbers provides a natural estimate of the variance of the overall stopping variable without compromising much on the performancecharacteristics of the estimation rules.

Robust tests in group sequential analysis: One- and two-sided hypotheses in the linear model

Abstract: Consider the linear modelY=Xθ+E in the usual matrix notation where the errors are independent and identically distributed. We develop robust tests for a large class of one- and two-sided hypotheses about θ when the data are obtained and tests are carried out according to a group sequential design. To illustrate the nature of the main results, let\(\hat \theta\) and\(\tilde \theta\) be anM- and the least squares estimator of θ respectively which are asymptotically normal about θ with covariance matrices σ2(XtX)−1 and τ2(XtX)−1 respectively. Let the Wald-type statistics based on\(\hat \theta\) and\(\tilde \theta\) be denoted byRW andW respectively. It is shown thatRW andW have the same asymptotic null distributions; here the limit is taken with the number of groups fixed but the numbers of observations in the groups increase proportionately. Our main result is that the asymptotic Pitman efficiency ofRW relative toW is (σ2/τ2). Thus, the asymptotic efficiency-robustness properties of\(\hat \theta\) relative to\(\tilde \theta\) translate to asymptotic power-robustness ofRW relative toW. Clearly, this is an attractive result since we already have a large literature which shows that\(\hat \theta\) is efficiency-robust compared to\(\tilde \theta\). The results of a simulation study show that with realistic sample sizes,RW is likely to have almost as much power asW for normal errors, and substantially more power if the errors have long tails. The simulation results also illustrate the advantages of group sequential designs compared to a fixed sample design, in terms of sample size requirements to achieve a specified power.