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Showing papers by "Pranab Kumar Sen published in 1979"


Journal ArticleDOI
TL;DR: In this paper, the robustness property of the preliminary test estimator when the assumed restraints may not hold was analyzed for a general multi-sample parametric model and compared with the parallel expressions for the unrestricted and restricted maximum likelihood estimators.
Abstract: Along with the asymptotic distribution, expressions for the asymptotic bias and asymptotic dispersion matrix of the preliminary test maximum likelihood estimator for a general multi-sample parametric model (when the null hypothesis relating to the restraints on the parameters may not hold) are derived and compared with the parallel expressions for the unrestricted and restricted maximum likelihood estimators. This study reveals the robustness property of the preliminary test estimator when the assumed restraints may not hold.

135 citations


01 Jun 1979
TL;DR: In this paper, an asymptotically risk-efficient sequential point estimation of regular functionals of distribution functions based on U-statistics is considered under appropriate regularity conditions.
Abstract: Asymptotically risk-efficient sequential point estimation of regular functionals of distribution functions based on U-statistics is considered under appropriate regularity conditions. Some auxiliary results on U-statistics are also considered in this context.

56 citations


Journal ArticleDOI
TL;DR: In this paper, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered, along with the asymptotic distribution of these estimators.

29 citations


Journal ArticleDOI
TL;DR: In this article, the maximum likelihood estimators of the parameters and the associated large sample covariance matrix are derived for a censored sample from a bivariate normal distribution consisting of the first k of n-order statistics of one variable and the induced order statistics of the other variable.
Abstract: SUMMARY For a censored sample from a bivariate normal distribution consisting of the first k of n order statistics of one variable and the induced order statistics of the other variable, the maximum likelihood estimators of the parameters and the associated large sample covariance matrix are derived. The likelihood ratio test for independence is also given and its power properties studied. These methods are useful in selection problems or in life testing situations in which concomitant variates are observable only for the uncensored primary variates.

28 citations


Journal ArticleDOI
TL;DR: For progressive censoring schemes pertaining to a general class of (parametric as well as nonparametric) testing situations, one encounters a (partial) sequence of linear combinations of functions of order statistics where the coefficients are themselves stochastic variables as mentioned in this paper.
Abstract: For progressive censoring schemes pertaining to a general class of (parametric as well as nonparametric) testing situations, one encounters a (partial) sequence of linear combinations of functions of order statistics where the coefficients are themselves stochastic variables. Weak convergence of such a quantile process to an appropriate Gaussian function is studied here, and the same is incorporated in the formulation of suitable (time-) sequential tests based on these quantile processes.

21 citations



Journal ArticleDOI
TL;DR: In this article, an estimator of the asymptotic variance of (a randomly stopped) linear combination of a function of order statistics is considered and its normality is studied under appropriate regularity conditions.
Abstract: An estimator of the asymptotic variance of (a randomly stopped) linear combination of a function of order statistics is considered and its asymptotic normality is studied under appropriate regularity conditions. A comparative study of the regularity conditions pertaining to the asymptotic normality and strong convergence of linear combinations of functions of order statistics and their estimated asymptotic variances is also made.

10 citations


Journal ArticleDOI
TL;DR: In this paper, progressively censored tests for a simple regression model based on weighted empirical distributions are considered for ungrouped as well as grouped data situations, and early decision rules based on such tests are formulated.
Abstract: In the context of time-sequential studies, progressively censored tests for a simple regression model based on weighted empirical distributions are considered for ungrouped as well as grouped data situations. Early decision rules based on such tests are formulated. The asymptotic theory of the proposed tests rests on a construction of suitable empirical processes and their convergence (in distribution) to appropriate Gaussian functions. Critical values of the proposed test statistics are obtained by simulation, For a hypothetical example (of practical interest), a comparative study is made for the empirical powers and stopping times for some rival tests.

9 citations


Journal ArticleDOI
TL;DR: In clinical trials and life testing problems, often, progressive censoring schemes are adopted to monitor the experiment from the beginning with the objective of a possible early termination as discussed by the authors, which is called early termination.
Abstract: In clinical trials and life testing problems, often, progressive censoring schemes are adopted to monitor the experiment from the beginning with the objective of a possible early termination. Progr...

7 citations


Journal ArticleDOI
TL;DR: In this paper, the classical two-sample problem is extended to the case where the distribution functions of the observable random variables are specified functions of unknown distribution functions and the null hypotheses to be tested or the parameters to be estimated relate to these unknown distributions.

4 citations


Journal ArticleDOI
TL;DR: For a general class of nonparametric analysis of covariance problems (with stochastic covariates), some repeated significance testing procedures are developed as mentioned in this paper, which rest on the construction of suitable rank order statistics based on the partial sequence of sample sizes and allow for a monitoring of experimentation with the objective of a possible early termination of experimentation.
Abstract: For a general class of nonparametric analysis of covariance problems (with stochastic covariates), some repeated significance testing procedures are developed. These procedures rest on the construction of suitable rank order statistics based on the partial sequence of sample sizes and allow for a monitoring of experimentation with the objective of a possible early termination of experimentation. The basic theory is based on the weak convergence of certain stochastic processes relating to the rank order statistics. Various properties of the proposed tests are discussed.

01 Jan 1979
TL;DR: In this article, a variety of models (depending on the nature of dependence of the two variates) is considered and the regularity conditions are tailored for these diverse situations. And some weak as well as strong invariance principles for these statistics are established.
Abstract: SUMMARY Along with the affinity of mixed rank statistics and linear combinations of induced order statistics, some weak as well as strong invariance principles for these statistics are established. ~l variety of models (depending on the nature of dependence of the two variates) is considered and the regularity conditions are tailored for these diverse situations. Some applications to some problems in statistical inference are also stressed.