Showing papers by "Pranab Kumar Sen published in 1977"
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TL;DR: For a broad class of jackknife statistics, it was shown in this article that the Tukey estimator of the variance converges almost surely to its population counterpart, and that the usual invariance principles (relating to the Wiener process approximations) usually filter through jackknifing under no extra regularity conditions.
Abstract: For a broad class of jackknife statistics, it is shown that the Tukey estimator of the variance converges almost surely to its population counterpart. Moreover, the usual invariance principles (relating to the Wiener process approximations) usually filter through jackknifing under no extra regularity conditions. These results are then incorporated in providing a bounded-length (sequential) confidence interval and a preassigned-strength sequential test for a suitable parameter based on jackknife estimators.
72 citations
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TL;DR: For general multivariate linear models, a composite hypothesis does not usually induce invariance of the joint distribution under appropriate groups of transformations, so that genuinely distribution-free tests do not usually exist.
Abstract: For general multivariate linear models, a composite hypothesis does not usually induce invariance of the joint distribution under appropriate groups of transformations, so that genuinely distribution-free tests do not usually exist For this purpose, some aligned rank order statistics are incorporated in the proposal and study of a class of asymptotically distribution-free tests Tests for the parallelism of several multiple regression surfaces are also considered Finally the optimal properties of these tests are discussed
44 citations
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TL;DR: In this article, the convergence of generalized $U$-statistics and von Mises' differentiable statistical functions is studied with the help of the general $L \log L$ martingale convergence theorem.
Abstract: Almost sure convergence of generalized $U$-statistics and von Mises' differentiable statistical functions is studied with the help of the general $L \log L$ martingale convergence theorem.
36 citations
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TL;DR: In this article, the authors obtained exact and asymptotic expressions for the joint distribution of correlated quadratic forms when the underlying distribution is a multivariate normal, which is the case in this paper.
35 citations
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TL;DR: For independent random variables distributed symmetrically around an unknown location parameter, aligned rank order statistics are constructed by using an estimator of the location parameter based on suitable rank statistics as discussed by the authors.
Abstract: For independent random variables distributed symmetrically around an unknown location parameter, aligned rank order statistics are constructed by using an estimator of the location parameter based on suitable rank statistics. The sequence of these aligned rank order statistics is then incorporated in the construction of suitable stochastic processes which converge weakly to some Gaussian functions, and, in particular, to tied-down Wiener processes in the most typical cases. The results are extended for contiguous alternatives and then applied in two specific problems in nonparametric inference. First, the problem of testing for shift at an unknown time point is treated, and then, some sequential type asymptotic nonparametric tests for symmetry around an unknown origin are considered.
25 citations
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TL;DR: For grouped data under time-sequential studies, a general class of progressively censored rank order tests for the simple regression model is proposed and studied in this paper, where asymptotic properties of these tests are studied through the formation of suitable stochastic processes having asymptic Gaussian structures.
Abstract: For grouped data under time-sequential studies, a general class of progressively censored rank order tests for the simple regression model is proposed and studied. Asymptotic properties of these tests are studied through the formation of suitable stochastic processes having asymptotic Gaussian structures. Some numerical illustrations are provided at the end.
10 citations
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TL;DR: In this paper, a weak convergence of the corresponding empirical process to a Gaussian process has been established by assuming that the sufficient statistics are $U$-statistics and utilizing certain results on the convergence of conditional expectations of functions of function of $U$, along with the functional central limit theorems for (reverse) martingales by Loynes and Brown.
Abstract: Under the condition that the minimal sufficient statistics are transitive, the sequence of Rao-Blackwell estimators of distribution function has been shown to form a reverse martingale sequence. Weak convergence of the corresponding empirical process to a Gaussian process has been established by assuming that the sufficient statistics are $U$-statistics and utilizing certain results on the convergence of conditional expectations of functions of $U$-statistics along with the functional central limit theorems for (reverse) martingales by Loynes (1970) and Brown (1971).
8 citations
01 May 1977
TL;DR: In this article, a class of analysis of covariance tests based on suitable linear rank statistics is proposed and studied, and some invariance principles for certain (multivariate) progressively censored rank order processes are established and incorporated in the study of the proposed tests.
Abstract: : In the context of survival analysis under a progressive censoring scheme, a class of analysis of covariance tests based on suitable linear rank statistics is proposed and studied. Some invariance principles for certain (multivariate) progressively censored rank order processes are established and incorporated in the study of the asymptotic properties of the proposed tests. (Author)
6 citations
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TL;DR: In this paper, the authors studied the properties of sample extreme values in the regular case and modified them for a modified version of the classic jackknifing technique, and some applications were also considered.
Abstract: : Sample extreme values are biased estimators of the end-points of a distribution, and hence, jackknifing is useful. However, the properties of jackknifing in such a case differ considerably from those in the regular case. These are studied here. Along with a modification of jackknifing, some applications are also considered. (Author)
1 citations