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Showing papers by "Pranab Kumar Sen published in 1982"


Journal ArticleDOI
TL;DR: In this article, a general class of recursive residuals is defined by means of lower-triangular, orthonormal transformations, and some weak invariance principles are established under appropriate regularity conditions.
Abstract: A general class of recursive residuals is defined by means of lower-triangular, orthonormal transformations. For these residuals, some weak invariance principles are established under appropriate regularity conditions. The theory is then incorporated in the study of robustness of some tests for change of parameters occurring at unknown time points.

65 citations


Journal ArticleDOI
TL;DR: In this paper, some tests based on residuals using M-estimators are considered and their asymptotic properties are studied for subhypothesis testing in some general linear models.
Abstract: SUMMARY For subhypothesis testing in some general linear models, some tests based on residuals using M-estimators are considered and their asymptotic properties are studied.

63 citations



Journal ArticleDOI
TL;DR: In this article, uniform integrability and moment convergence of (non-sequential) M- and L-estimators are established, and various properties of their sequential versions are studied.
Abstract: In the context of asymptotically minimum risk (sequential) point estimation of location of a symmetric distribution, M-and L-estimators are considered, and various properties of their sequential versions are studied. Asymptotic distributions of he allied stopping times are also derived. In this study, uniform integrability and moment convergence of (non-sequential) M- and L-estimators are established. These results have interest of therir own and provide the main tools for the proof of the other results presented. For the sequential estimators, their asymptotic risk efficiencies are shown to coincide with the asymptotic efficiencies of the respective non-sequential estimators; this enables one to construct the asymptotically minimax sequential M- and L-estimators in the model of contaminancy. Parallel results also hold for the rank estimators of location.

14 citations


Journal ArticleDOI
TL;DR: In this paper, invariance principles for least squares estimators and some aligned rank statistics are studied and incorporated in the formulation and study of the asymptotic properties of some tests for a possible change in a (multiple-) regression relationship occuring at an unknown time point.
Abstract: Some invariance principles for least squares estimators and some aligned rank statistics are studied and incorporated in the formulation and study of the asymptotic properties of some tests for a possible change in a (multiple-) regression relationship occuring at an unknown time point. Allied efficiency results are also studied.

10 citations


Journal ArticleDOI
TL;DR: In this paper, a set of hypothesis testing problems for the p responses q-sample model is presented, where it is a priori assumed that the response-sample interactions are null.

8 citations


Journal ArticleDOI
TL;DR: In this article, a renewal theorem relating to some stopping times is established for an urn model (arising typically in the sequential estimation of the size of a finite population), along with an invariance principle for a partial sequence of nonnegative random variables, a representation of these random variables in terms of linear combinations of some martingaledifferences provides the key to a simple solution.
Abstract: For an urn model (arising typically in the sequential estimation of the size of a finite population), along with an invariance principle for a partial sequence of nonnegative random variables, a renewal theorem relating to some stopping times is established A representation of these random variables in terms of linear combinations of some martingale-differences provides the key to a simple solution 1 Introduction The following urn model arises typically in the sequential estimation of the total size of a finite population An urn contains an unknown number N of white balls and no others We repeatedly draw a ball at random, observe its color and replace it by a black ball, so that before each draw, there are N balls in the urn Let W,, be the number of white balls observed in the first n draws, n -1 (Wo = 0, Wi X 1 and W1k ' k, k - 2) For large N (and n, satisfying n/N -o a: 0 0, consider the stopping variable

6 citations


Journal ArticleDOI

5 citations


Journal ArticleDOI
TL;DR: In this paper, the problem of testing a general parametric hypothsis following a preliminary test on some other parametric restraints is considered, which is based on appropriate likelihood ratio statistics.
Abstract: The problem of testing a general parametric hypothsis following a preliminary test on some other parametric restraints is considered. These tests are based on appropriate likelihood ratio statistics. The effect of the preliminary test on the size and power of the ultimate test is studied. In this context, some asymptotic distributional properties of some likelihood ratio statistics are studied and incorporated in the study of the main results. 1 . Introduction In a parametric model, the underlying distribution are of assumed forms and the parameter θ belongs to a parameter * Work supported by the National Heart, Lung and Blood Institute, Contract NIH-NHLBI-71-2243-L from the National Institutes of Health. AMS 1980 classifications. 62 Ε 20

3 citations



Journal ArticleDOI
TL;DR: In this paper, a maximal distance statistic, based on the generalized pair chart, has been considered for testing the hypothesis of equality of the two distributions, and an alternative pair chart based on partial observations is also considered.
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.

Journal ArticleDOI
TL;DR: Based on two-sample rank order statistics, a repeated significance testing procedure for a multi-sample location problem is considered in this article, where the asymptotic distribution theory of the proposed tests is given under the null hypothesis as well as under local alternatives.


Journal ArticleDOI
TL;DR: For independent (but not necessarily identically distributed) random variables with distributions symmetric about the respective medians (means), the expected value of the sample range is a minimum when these means are all equal as mentioned in this paper.

01 Jan 1982
TL;DR: In this article, a method of estimating the index parameter of a stable distribution is considered based on the sample characteristic function, and weak convergence of the empirical characteristic function (process) is incorporated in the choice of an asymptotically optimal estimator.
Abstract: Based on the sample characteristic function, a method of estimatingthe index parameter of a stable. distribution is considered. Weak convergence of the empirical characteristic function (process) is incorporated in the choice of an asymptotically optimal estimator and in the study of its asymptotic properties.