Showing papers by "Pranab Kumar Sen published in 1985"

On Some Shrinkage Estimators of Multivariate Location

Abstract: For a continuous and diagonally symmetric multivariate distribution, incorporating the idea of preliminary test estimators, a variant form of the James-Stein type estimation rule is used to formulate some shrinkage estimators of location based on rank statistics and $U$-statistics. In an asymptotic setup, the relative risks for these shrinkage estimators are shown to be smaller than their classical counterparts.

On shrinkage m-estimators of location parameters

Abstract: For a general class of continuous ( and marginally symmetric ) inultivariate distributions, based on suitable M-statistics ( involving bounded but possibly discontinuous score generating functions), shrinkage estimators of location are considered. These estimators are based on the James-Stein type rule and incorporates the idea of preliminary test estimation too. The main emphasis is laid on the study of asymptotic tdistributional ) risk properties of these est-innators, and asymptotic tin-) adraissibility results are also studied under fairly general regularity conditions.

Asymptotic equivalence of the harrell-davis median estimator and the sample median

Abstract: This paper presents an asymptotic equivalence result with a sharp rate of convergence forthe sample median and the Harrell-Davis median estimator. The consequences of this result are discussed.

Nonparametric testing against restricted alternatives under progressive censoring

Abstract: Nonparametric testing procedures under progressive censoring schemes are often adopted in clinical trials and life testing experimentations. In a variety of situations, a null hypothesis (of the homogeneity of distributions) may be tested against a restricted viz., orthant or ordered alternative. Though such tests in a general setup have been considered in a complete sample or a single point censored (or truncated) experimental scheme, there has not been much progress with these tests in a progressively censored setup. Genuinely distribution free tests based on simple linear rank statistics and the classical union intersection principle are considered. The theory of such time sequential tests rests heavily on some basic invariance principles, and these are studied as well. The case of proportional hazard models is also treated briefly. The main emphasis is laid on the development of the relevant asymptotic theory, and in this context, some (sub) martingale characterizations of progressively censored rank ...

Asymptotic relative efficiency of multivariate m-estimators

Abstract: Asymptotic Relative Efficiencies (ARE) of the robust coordinatewise M-estimators with respect to the robust Maronna-type M-estimators proposed by Singer and Sen (1985) are computed under different elliptically symmetric error distributions. ARE of robust coordinatewise M-estimators with respect to Normal Maximum Likelihood (NML) estimators are also computed under a more general bivariate underlying distribution. The results indicate that the Maronna-type M-estimator is only slightly more efficient than the coordinatewise one, except for extreme cases like the Cauchy or for large dimensionalities where the gain in efficiency may be considerable. Both types of M-estimators perform better than the NML estimators for the proposed departures from normality. For distributions not of the elliptically symmetric type, Maronna-type estimators are not suitable, and hence, the comparison is not of real interest.

On least squares estimation of intercepts after a preliminary test on parallelism of regression lines

Abstract: For the several sample (simple) regression model, the problem of estimating the intercept parameters following a preliminary test on parallelism of the regression lines is treated. Least squares estimators of the intercepts are considered for the models with uncertain prior information on the homogeneity of the regression parameters, and various properties of these estimators are studied. The conventional least squares estimators are also considered along with the allied asymptotic efficiency results are studied.

Extreme value theory for certain non-stationary sequences1

Abstract: Summary Under a Markovian structure on a sequence of random variables which can be partitioned into m(1) jointly dependent subsequences (where within each subsequence the random variables have a common marginal distribution which may vary between the subsequences), the asymptotic distribution theory of the sample extreme values is developed. The asymptotic independence of the subsequence extreme values is also studied.

Tests of homogeneity of intercepts after a preliminary test

Abstract: For the multl-sample regression model , the problem of testing equality of intercepts following a preliminarytest on the equality o f slopes is considered. The t e s t s are based on the conventional least squares estimators (without necessarily assuming the normality of the underlying error distributions ) , and the impact of a preliminary test on the asymptotic size and power of the final test is studied.

On progressively truncated maximum likelihood estimators

Abstract: The basic regularity conditions pertaining to the asymptotic theory of progressively truncated likelihood functions and maximum likelihood estimators are considered, and the uniform strong consistency and weak convergence of progressively truncated maximum likelihood estimators are studied systematically.

Asymptotic relative efficiency of some joint-tests for location and scale parameters based on selected order statistics

Abstract: For a location-scale distribution, based on few selected order statistics, joint-tests for the location and scale parameters are considered. In the light of the asymptotic relative efficiency results, optimal spacings of the order statistics are studies (and their duality to the estimation problem is discussed).