scispace - formally typeset
Search or ask a question

Showing papers by "Pranab Kumar Sen published in 1988"


Journal ArticleDOI
TL;DR: In this paper, a technique de jackknife is proposed for estimating the variance and representations of distributions asymptotiques du second-ordre for les estimateurs du jackknife classiques.
Abstract: On considere une technique de jackknife a deux niveaux pour l'estimation de la variance et des representations de distributions asymptotiques du second-ordre pour les estimateurs du jackknife classiques

41 citations


Book ChapterDOI
TL;DR: In finite population sampling, the sampling frame defines the units and the size of the survey population from which the sample is taken unambiguously, and reconstructs a population having an uncountable (or infinite) number of natural units in terms of a finite population by redefining suitable sampling units.
Abstract: Publisher Summary This chapter reviews some recent results in finite population asymptotics. In finite population sampling (FPS), the theory of objective or probabilistic sampling plays a fundamental role in statistical inference. In survey sampling, the sampling frame defines the units and the size of the survey population from which the sample is taken unambiguously. It also reconstructs a population having an uncountable (or infinite) number of natural units in terms of a finite population by redefining suitable sampling units. Resampling methods, including the jackknife and the bootstrap, can provide standard error estimates and nonparametric confidence intervals for the parameters of interest or approximate sampling distributions of statistics. The estimation of the total size of a population including, in particular, mobile populations such as the number of fish in a lake is of great importance in a variety of biological environmental and ecological investigations.

32 citations


01 Jan 1988
TL;DR: In this paper, a conditional quantile function (of Z given X = x) is defined for a sequence of independent and identically distri buted (i.i.d.) random vectors with a distribution function (d.f.
Abstract: Let {(Xf, Zf), i > 1} be a sequence of independent and identically distri buted (i.i.d.) random vectors (r.v.) with a distribution function (d.f.) n(x9z), (x,z) e R2 ( ? (?oo, oo)2). Let F(x) = n(x, oo), xeR, and let G(z\x) be the conditional d.f. of Z given X = x, for zeR, xeR. A conditional quantile function (of Z given X = x) is defined by

28 citations


Journal ArticleDOI
TL;DR: In this article, the harmonic income gap ratio and the harmonic Gini coefficient play important roles in the formulation and meaningful interpretation of affluence indexes, and the Gastwirth coefficient is also very pertinent in this context.

18 citations


Journal ArticleDOI
TL;DR: In this article, the union intersection (UI-) principle and the theory of M-estimation of location are incorporated in the formulation of some robust, preliminary test, isotonic (M−) estimators of locations.

7 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the multivariate simple location model under an orthant restriction on the parameters and derived an estimator under the null hypothesis as well as a sequence of local alternatives.
Abstract: Isotonic M-estimation of location parameters in the multivariate simple location model is considered under an orthant restriction on the parameters. The union-intersection principle and theory of M-estimation of location are incorporated in the formulation of some robust preliminary test and the derived estimator is studied under the null hypothesis as well as a sequence of local alternatives.

3 citations




Journal ArticleDOI
TL;DR: In this paper, the authors considered three simple random sampling strategies: (i) with replacement, mean per unit estimation, (ii) without replacement and (iii) mean per distinct unit estimation and showed that the second strategy still fares better than the first, although the third strategy may not perform better than second one.
Abstract: Bounded risk estimation of the mean of a finite population is considered under three simple random sampling strategies: (i) with replacement, mean per unit estimation, (ii) with replacement, mean per distinct unit estimation, and (iii) without replacement, mean per unit estimation. It is well known that in the fixed sample size scheme, (iii) fares better than (ii) and (ii) better than (i). However, in the current context, the sample sizes are dictated by (possibly, degenerate) stopping times, and visualizing the cost (due to measurements/recording, etc.) as a function of the number of distinct units in the sample, it is shown that the second strategy still fares better than the first, although the third strategy may not perform better than the second one. Actually, in the case of known population variance, it is shown that in the light of the number of distinct units, the difference of ASN for the second and third strategies can never be greater than two or less than minus one. A similar relationship also...

2 citations