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Showing papers by "Pranab Kumar Sen published in 1986"



Journal ArticleDOI
TL;DR: In this article, a censored version of the classical Gini coefficient (G) is incorporated in the formulation of various poverty indexes, i.e., the average income gap of the poor people from the poverty line ω, taken as a ratio to ω itself.
Abstract: Poverty is usually defined as the extent to which individuals in a society or community fall below a minimal acceptable standard of living. An index of poverty is generally based on the proportion (α) of the poor people and their income distribution through the income gap ratio (β) (i.e., the average income gap of the poor people from the poverty line ω, taken as a ratio to ω itself) and other measures of income inequalities. In this context, the well-known Gini coefficient of income inequality plays a vital role. In view of the fact that the poverty indexes all relate to the income pattern of the poor, interpreted in some way or other, usually a censored (Gω) or truncated (G α) version of the classical Gini coefficient (G) is incorporated in the formulation of such indexes. Among the various poverty indexes, πA = αβ, πτ = Gc ω, and πs=α{β+(1-β)Gα} have been used more extensively than the others. Although each of π S and π T is justified on the grounds of certain plausible axioms, from a statisti...

43 citations


Journal ArticleDOI
TL;DR: In this article, a general formulation of shrinkage R-estimation is considered for a multiple regression model, bearing the plausibility of a subset of the regression parameters being close to a pivot, for the complementary subset, based on the usual James-Stein rule.
Abstract: For a multiple regression model, bearing the plausibility of a subset of the regression parameters being close to a pivot, for the complementary subset, based on the usual James-Stein rule, a general formulation of shrinkage R-estimation is considered. In the light of asymptotic distributional risks of estimators, performance characteristics ( under local alternatives) of the classical R-est-imator and its preliminary test and shrinkage versions (all based on the common score function ) are studied. These shed light on the relative dominance picture in a meaningful asymptotic setup.

16 citations


Journal ArticleDOI
TL;DR: In this article, the shrinkage least squares estimators of intercepts based on the James-Stein rule on regression slopes are considered and relative pictures on the (asymptotic) risk of the classical, preliminary test and the shrinking-least-squares estimators are presented.
Abstract: In a multi-sample simple regression model, generally, homogeneity of the regression slopes leads to improved estimation of the intercepts. Analogous to the preliminary test estimators, (smooth) shrinkage least squares estimators of Intercepts based on the James-Stein rule on regression slopes are considered. Relative pictures on the (asymptotic) risk of the classical, preliminary test and the shrinkage least squares estimators are also presented. None of the preliminary test and shrinkage least squares estimators may dominate over the other, though each of them fares well relative to the other estimators.

14 citations



Journal ArticleDOI
TL;DR: Two types of multivariate M-estimators of the parameter matrix in the standard growth curve model are obtained via the Potthoff-Roy transformation as discussed by the authors, and their asymptotic distributions are derived through an extension of the methods considered in Singer and Sen (1985) and computational algorithms are suggested.

13 citations


Journal ArticleDOI
TL;DR: In this article, a general class of permutationally distribution-free rank tests for the ordered alternative problem is considered and the theory of covariance model is supplemented by numerical studies.
Abstract: For an analysis of covariance model (pertaining to completely randomized as well as complete block designs) based on the union-intersection principle, a general class of permutationally distribution-free rank tests for the ordered alternative problem is considered. The theory is supplemented by numerical studies.

10 citations


Journal ArticleDOI
TL;DR: In this article, the orthonormal Legendre polynomial system is incorporated in the formulation of signed rank statistics for asymptotic efficient testing and estimation procedures for the location parameter (or the intercept parameter in a linear model).
Abstract: The orthonormal Legendre polynomial system is incorporated in the formulationf of signed rank statistics for asymptoticaly efficient testing and estimation procedures for the location parameter (or the intercept parameter in a linear model). A well defined stopping rule relates to an adaptive, sequential procedure for the choice of a finite set of terms and the related score function. Some refined asymptotic linearity results( in location as well as regression parameters) on signed rank staistics (with reference to the Legendre polynomial system) are established, and their role in the proposed (sequentially adaptive) procedure is thoroughly discussed.

9 citations


Book ChapterDOI
01 Jan 1986
TL;DR: In this article, the authors systematically reviewed the literature in the context of sequential (point as well as interval) estimation of the size of a population, with special emphasis placed on appropriate martingale constructions for suitable sequences of statistics arising in this context, invariance principles for sequential tagging are considered.
Abstract: SUMMARY For the estimation of the total number of individuals in a finite population, the capture, mark, release and recapture method and its variants for inverse as well as sequential sampling schemes have been extensively worked out in the literature. These are systematically reviewed in the context of sequential (point as well as interval) estimation of the size of a population. With special emphasis placed on appropriate martingale constructions for suitable sequences of statistics arising in this context, invariance principles for sequential tagging are considered, and their role in the proposed sequential analysis is critically discussed.

5 citations


Journal ArticleDOI
TL;DR: In this paper, a critical appraisal of this basic role of jackknifing in shrinkage estimation is made and the usual versions of jack-knifed shrinkage estimates are considered and their performance characteristics are studied.
Abstract: In multi-parameter ( multivariate ) estimation, the Stein rule provides minimax and admissible estimators , compromising generally on their unbiasedness. On the other hand, the primary aim of jack-knifing is to reduce the bias of an estimator ( without necessarily compromising on its efficacy ), and, at the same time, jackknifing provides an estimator of the sampling variance of the estimator as well. In shrinkage estimation ( where minimization of a suitably defined risk function is the basic goal ), one may wonder how far the bias-reduction objective of jackknifing incorporates the dual objective of minimaxity ( or admissibility ) and estimating the risk of the estimator ? A critical appraisal of this basic role of jackknifing in shrinkage estimation is made here. Restricted, semi-restricted and the usual versions of jackknifed shrinkage estimates are considered and their performance characteristics are studied . It is shown that for Pitman-type ( local ) alternatives, usually, jackkntfing fails to prov...

4 citations


01 Jan 1986
TL;DR: In this paper, shrinkage and preliminary test estimator versions of U-statistics are considered for the (multi-parameter) minimum risk sequential estimation problem and related asymptotic risk-efficiency results are also considered.
Abstract: For general estimable parameters in a nonparametric setup, shrinkage (Stein-rule) and preliminary test estimator versions of U-statistics are considered for the (multi-parameter) minimum risk sequential estimation problem. In the usual fashion, allowing the cost per unit sample to be small, an asymptotic model is framed, and in this setup, the asymptotic distributional risks of these versions of (sequential) U-statistics are studied. Related asymptotic risk-efficiency results are also considered.


Journal ArticleDOI
TL;DR: In this paper, an alternative (permutationally) distribution-free test for the null hypothesis of no treatment effect in the mixed-model experiment was proposed, which utilizes the inherent invariance structure in a more visable and direct way.
Abstract: Nonparametric tests for the null hypothesis of no treatment effect in the mixed-model experiment which involves n randomly chosen subjects who respond once to each of ρ distinct treatments have been developed by Koch and Sen (1968), These tests were based on the assumption of compound symmetry of the error vectors and on the weaker assumption of diagonal symmetry of the error vectors. This paper considers an alternative (permutationally) distribution-free test under this latter assumption. The new test follows the same type of distribution theory as those in Koch and Sen, but utilizes the inherent invariance structure in a more visable and direct way.

Journal ArticleDOI
TL;DR: Stable laws for M-estimators, maximum likelihood and other estimators were obtained through parallel results for the estimating functions and relative compactness of some related estimating functional processes.
Abstract: Stable laws forM-estimators, maximum likelihood and other estimators and obtained through parallel results for the estimating functions and relative compactness of some related estimating functional processes.

Journal ArticleDOI
TL;DR: In this article, a nonparametric symmetric unbiased estimator of the generalized variance is considered, and it is shown to be (nonparametric) optimal for the class of distributions having finite fourth order moments.
Abstract: : For multivariate distributions with finite second order moments, a nonparametric symmetric, unbiased estimator of the generalized variance is considered, and it is shown to be (nonparametric) optimal for the class of distributions having finite fourth order moments. A jackknifed version of the sample generalized variance is also considered as a contender; it is computationally more convenient and asymptotically equivalent to the former. It is also shown that the second estimator performs quite well (in large sample) relative to the optimal normal theory estimators under several loss functions. (Keywords: kernels; U-statistics; von mises' functionals).