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Showing papers by "Pranab Kumar Sen published in 1990"


Journal Article
TL;DR: In this paper, a method for the comparison of two linear forms of a common random vector under the criterion of Pitman's measure of closeness is given, assuming multivariate normality of the random vector, one can determine exact expressions for the closeness probabilities.
Abstract: A method is given for the comparison of two linear forms of a common random vector under the criterion of Pitman's measure of closeness. Assuming multivariate normality of the random vector, one can determine exact expressions for the closeness probabilities. The applicability of the theory is illustrated on the comparison of ridge regression estimators.

49 citations


Journal ArticleDOI
TL;DR: In this article, a method for the comparison of two linear forms of a common random vector under the criterion of Pitman's measure of closeness is given, assuming multivariate normality of the random vector, one can determine exact expressions for the closeness probabilities.
Abstract: A method is given for the comparison of two linear forms of a common random vector under the criterion of Pitman's measure of closeness. Assuming multivariate normality of the random vector, one can determine exact expressions for the closeness probabilities. The applicability of the theory is illustrated on the comparison of ridge regression estimators.

32 citations


Journal ArticleDOI
TL;DR: In this paper, the asymptotic distribution of n(Mn(1)-Mn) is studied; it is typically non-normal and reveals the role of the initial estimator Mn(0).
Abstract: For a general (real) parameter, let Mnbe the M-estimator and Mn(1) be its one-step version (based on a suitable initial estimator Mn(0)). It is known that, under certain regularity conditions, n(Mn(1)-Mn)=Op(1). The asymptotic distribution of n(Mn(1)-Mn) is studied; it is typically non-normal and it reveals the role of the initial estimator Mn(0).

23 citations


Journal ArticleDOI
TL;DR: In this paper, the interrelationship of median unbiasedness and the Pitman closeness of (sequential) estimators is examined thoroughly for a general class of stopping rules, and it is also shown that sequential shrinkage estimators of the multinormal mean (vector) dominate the classical (semi-) maximum likelihood estimator.
Abstract: For a general class of stopping rules, the inter-relationship of median unbiasedness and the Pitman closeness of (sequential) estimators is examined thoroughly. It is also shown that in the light of the Pitman closeness, sequential shrinkage estimators of the multinormal mean (vector) dominate the classical (sequential) maximum likelihood estimator.

5 citations


Journal ArticleDOI
TL;DR: In this article, the canonical structure of a two-way contingency table is emphasized to derive union-intersection (Ul•) tests for independence between two categorical variables, and a sequential way for identifying the adequate model is presented.
Abstract: ABSTRACT: The canonical structure of a two‐way contingency table is emphasized to derive union‐intersection (Ul‐) tests for independence between two categorical variables. In this context, special attention has been paid to the so‐called step‐down procedure (which is a variant of the UI‐procedure Some properties of this procedure and computational algorithms are considered and a sequential way for identifying the adequate model is presented.

2 citations


01 Jan 1990
TL;DR: In this article, the optimality properties of Pitman estimators were studied with respect to the measure of the Pitman closeness of estimators, and they were shown to be translation-equivariant and optimality under quadratic loss.
Abstract: Pitman estimators of location are unbiased, translation-equivariant and possess some optimality properties under quadratic loss. Similar optimality properties of Pitman estimators are studied with respect to the measure of Pitman closeness of estimators.

Journal ArticleDOI
TL;DR: In this article, the rank order test under the null hypothesis of restricted interchangeability was proposed and the asymptotic relative efficiency of this nonparametric test in comparison with Votaw's (1948, Ann. Math. Statist, 19, 447,473) likelihood ratio test was given.
Abstract: Exact and large sample distributions of the rank order test under the null hypothesis of restricted interchangeability are obtained. Under given regularity conditions and under Pitman's shift in location alternative, the asymptotic relative efficiency of this nonparametric test in comparison with Votaw's (1948, Ann. Math. Statist., 19, 447–473) likelihood ratio test is given.