Showing papers by "Pranab Kumar Sen published in 1991"
Book•
24 Apr 1991
TL;DR: A formal theory in which optimal tests are derived for simple statistical hypotheses in such a framework was developed by Abraham Wald in the early 20th century as mentioned in this paper, where the sample size depends in a random manner on the accumulating data.
Abstract: Sequential analysis refers to the body of statistical theory and methods where the sample size may depend in a random manner on the accumulating data. A formal theory in which optimal tests are derived for simple statistical hypotheses in such a framework was developed by Abraham Wald in the early 1
349 citations
TL;DR: In this paper, a Cox-type parameterization of the stochastic intensity of a point process is considered and a sieve estimation procedure (Grenander, 1981) is used to estimate the coefficient.
164 citations
20 citations
TL;DR: It has been shown as mentioned in this paper that the remainder term of a form of the Taylor expansion, involving Hadamard derivative, of the statistical functional is asymptotically negligible, and this result is extended to a more general form with respect to weighted empirical processes in order to establish some (uniform) linear functional approximations, which is usually needed for drawing statistical conclusions.
18 citations
TL;DR: In 1990, the students' committee consisting of Tumulesh Solanky (Chair), Tai-Ming Lee and Saibal Chattopadhyay had invited Professors Peter Kempthorne, Pranab K. Sen and Shelemyahu Zacks to serve as guest panelists.
Abstract: On May 4, 1990, the Students' Seminar Series of the Department of Statistics at the University of Connecticut organized a "Research Panel Discussion." The students' committee consisting of Tumulesh Solanky (Chair), Tai-Ming Lee and Saibal Chattopadhyay had invited Professors Peter Kempthorne, Pranab K. Sen and Shelemyahu Zacks to serve as guest panelists. Professor Nitis Mukhopadhyay served as the moderator. The informal discussion touched upon many interesting aspects of statistical research and education. The varied opinions and comments of these expert panelists were undoubtedly most informative to the audience present that day, and it is hoped that such comments will also prove to be useful in the future for the general audience. What follows is a slightly edited version of the proceedings of that lively panel discussion.
7 citations
TL;DR: In this paper, the weak convergence of certain randomly weighted residual empirical processes in the first-order autoregression model to a continuous Gaussian process is proved. And the result is used to derive the asymptotic uniform linearity of the given processes and of certain class of linear rank statistics based on the residuals in the estimated parameters.
Abstract: This paper proves the weak convergence of certain randomly weighted residual empirical processes in the first order autoregression model to a continuous Gaussian process. The result is used to derive the asymptotic uniform linearity of the given processes and of certain class of linear rank statistics based on the residuals in the estimated parameters. These latter results are used to study the asymptotic behavior of certain goodness-offit tests and R-estimators of the autoregression parameter. AMS 1980 subject classifications: Primary 60 Β 10, secondary 62 E 20, 62 M 10
6 citations
TL;DR: For the multivariate normal mean (vector) estimation problem, some characterizations of the Pitman closest property of a general class of Stein-rule estimators (including the so-called positive-rule versions) are studied in this paper.
Abstract: For the multivariate normal mean (vector) estimation problem, some characterizations of the Pitman closest property of a general class of shrinkage (or Stein-rule) estimators (including the so called positive-rule versions) are studied. Further, for the same model when the parameter is restricted to a positively homogeneous cone, Pitman closeness of restricted shrinkage maximum likelihood estimators is established.
6 citations
TL;DR: A panel discussion including an introduction by Sen, a paper by Keating and Mason, and a second one by Sen on recent developments in Pitman closeness and its applications and some final remarks by Rao.
5 citations
TL;DR: For the model X ∼ Np: (θ,I)preliminary test estimator (PTE), shrinkage and positive-rule versions of the MLE (X) of θ are mutually compared in the light of the Pitman closeness measure.
Abstract: For the model X ∼ Np: (θ,I)preliminary test estimator (PTE), shrinkage and positive-rule versions of the MLE (X) of θare mutually compared in the light of the Pitman closeness measure. The usual dominance properties of these estimators pertaining to the conventional quadratic loss criterion are shown to remain intact in the current context too. In an asymptotic setup, the conclusions hold for a much wider class of estimators pertaining to general parametric and nonparametric models.
4 citations
TL;DR: In this article, the authors compared equivariant estimators of the dispersion matrix of a multivariate normal population using the generalized Pitman nearness criterion based on the entropy loss function.
Abstract: Some equivariant estimators of the dispersion matrix of a multivariate normal population are compared using the generalized Pitman nearness criterion based on the entropy loss function. It is shown that, under the group of lower triangular transformations, a best equivariant estimator does not exist. Existence of best estimators in certain subclasses are discussed and the performances of two commonly used estimators are compared. Some properties of central chi-square distributions are obtained and used to derive the main results.
4 citations
TL;DR: In this article, the authors considered the effect of the underlying trait distributions for the different treatment groups for an experiment with multiple treatment groups and a historical control group, and applied statistical tests for an increasing trend in proportion (across the treatment groups) are considered.
TL;DR: In this paper, Roy's union intersection principle is incorporated in a formulation of suitable isotonic M-procedures for the preliminary testing component, following which M-estimator of location are presented in the same vein.
Abstract: For the usual multivariate linear model, preliminary test Mestimation theory is considered in an isotonic setup. Roy's union-intersection principle is incorporated in a formulation of suitable isotonic M-procedures for the preliminary testing component, following which M-estimator of location are presented in the same vein. The main thrust is on the development of the related asymptotic theory with a view to studying the allied robustness aspects. A numerical illustration is set to demonstrate the superiority of the proposed approach.