Showing papers by "Pranab Kumar Sen published in 1980"

Asymptotic theory of some tests for a possible change in the regression slope occurring at an unknown time point

Abstract: Based on least squares estimators and aligned rank order statistics, some testing procedures for a possible change in the regression slope occurring at an unknown time point are considered. The asymptotic theory of the proposed tests rests on certain invariance principles relating to least squares estimators and aligned rank order statistics, and these are developed here.

On Time-Sequential Point Estimation of the Mean of an Exponential Distribution

Abstract: In the context of a life testing problem, a time-sequential procedure for estimating the mean of an exponential distribution is proposed and is shown to be asymptotically risk-efficient. Asymptotic properties of the stopping number, stopping time and the total life under testing are also studied.

Limit Theorems for an Extended Coupon Collector's Problem and for Successive Subsampling with Varying Probabilites*

Abstract: Asymptotic normality as well as some weak invariance principles for bonus sums and waiting times in an extended coupon collector's problem are considered and incorporated in the study of the asymptotic distribution theory of estimators of (finite) population totals in successive sub-sampling (or multistage sampling) with varying probabilities (without replacement). Some applications of these theorems are also considered.

22 Nonparametric simultaneous inference for some MANOVA models

Abstract: Publisher Summary This chapter focuses on nonparametric simultaneous inference for some multivariate analysis of variance (MANOVA) models and presents simultaneous inference procedures based on general rank order statistics and derived estimators. One of the basic reasons for advocating the use of rank statistics and estimates is their good robustness against outliers and gross-errors. For nonparametric procedures considered in the chapter, any specific form of the underlying distributions (only continuity or sometimes symmetry suffices) is not required, and hence they enjoy a broader scope of applicability. They are robust. But, to meet this scope in full, the exact percentile points of the null distributions of various nonparametric statistics on which simultaneous procedures rest should be computed. For general rank statistics, these distributions can be enumerated by reference to suitable permutational invariance structures. The distributions of various nonparametric statistics are usually dominated by their asymptotic forms so that the use of asymptotic percentile points results in conservatism and does not affect the validity of these procedures. On the other hand, it leads to some loss in efficiency (or power); this loss is usually very small when sample sizes are large.

On Almost Sure Linearity Theorems for Signed Rank Order Statistics

Abstract: Almost sure asymptotic linearity of signed rank order statistic in shift parameter is studied under suitable regularity conditions and the results are extended to stationary $\phi$-mixing processes as well.

On the Pitman Efficiency of Sequential Tests

Abstract: The paper defines a new notion of Pitman efficiency of sequential tests and examines in the light of this notion the asymptotic relative efficiencies of some sequential rank order tests with respect to the sequential probability ratio tests and sequential likelihood ratio tests.