Showing papers by "Pranab Kumar Sen published in 1973"
TL;DR: In this article, a general class of rank order tests for progressive censoring is proposed along with a basic martinga:le property and a Brownian motion approximation for a related rank order process, asymptotic distribution theory of the proposed statistics is developed.
Abstract: SummaryProgressive censoring schemes (allowing a continuous monitoring of experimentation until a terminal decision is reached) are often adopted in clinical trials and life testing problems. In this paper, a general class of rank order tests for progressive censoring is proposed. Along with a basic martinga:le property and a Brownian motion approximation for a related rank order process, asymptotic distribution theory of the proposed statistics is developed. Asymptotic performance characteristics of the proposed tests (in the light of Bahadur efficiency and the stochastic smallness of the stopping variables) are studied.
88 citations
TL;DR: Inference procedures based on simple rank statistics are proposed and studied for the statistical analysis of longitudinal data in this article, which do not require the basic assumption of multivariate normality of the underlying distributions.
Abstract: Inference procedures based on some simple rank statistics are proposed and studied for the statistical analysis of longitudinal data. These robust and asymptotically efficient procedures do not require the basic assumption of multivariate normality of the underlying distributions. The theory is illustrated with two examples.
54 citations
TL;DR: In this paper, it was shown that the asymptotic probability of the classical Kolmogorov-Smirnov statistic exceeding any positive real number provides an upper bound for the corresponding probability when the underlying random variables are not necessarily identically distributed.
Abstract: For a sequence of random variables forming an $m$-dependent stochastic process (not necessarily stationary), asymptotic distribution and other convergence properties of the extremum of certain functions of the empirical distribution are studied. In this context, it is shown that the asymptotic probability of the classical Kolmogorov-Smirnov statistic exceeding any positive real number provides an upper bound for the corresponding probability when the underlying random variables are not necessarily identically distributed. The theory is specifically applied to the study of the limiting distribution, strong convergence and convergence of the first moment of the strength of a bundle of parallel filaments (which is shown to be the extremum of a function of the empirical distribution).
31 citations
TL;DR: For a set of independent but not necessarily identically distributed random variables, a simple Kolmogorov-Smirnov-type test was proposed for testing the hypothesis of symmetry as discussed by the authors.
Abstract: For a set of independent but not necessarily identically distributed random variables, a simple Kolmogorov-Smirnov-type test is proposed for testing the hypothesis of symmetry (about a common and specified point). The exact and asymptotic (null hypothesis) distributions of some allied statistics are obtained, and the Bahadur-efficiency of the test is studied.
24 citations
19 citations
TL;DR: Based on a Wiener process approximation, a sequential test for the bundle strength of filaments is proposed and studied in this article, and asymptotic expressions for the OC and ASN functions are derived.
Abstract: Based on a Wiener process approximation, a sequential test for the bundle strength of filaments is proposed and studied here. Asymptotic expressions for the OC and ASN functions are derived, and it is shown that asymptotically the test is more efficient than the usual fixed sample size procedure based on the asymptotic normality of the standardized form of the bundle strength of filaments,
14 citations
01 Jan 1973
13 citations
TL;DR: In this paper, the authors deal with the asymptotic theory of sequential confidence intervals of prescribed width $2d (d > 0) and prescribed coverage probability $1 - \alpha (0 < \alpha < 1) for the (unknown, per unit) strength of bundle of parallel filaments.
Abstract: The present paper deals with the asymptotic theory of sequential confidence intervals of prescribed width $2d (d > 0)$ and prescribed coverage probability $1 - \alpha (0 < \alpha < 1)$ for the (unknown, per unit) strength of bundle of parallel filaments. In this context, certain useful convergence results on the empirical distribution and on the bundle strength of filaments are established and incorporated in the proofs of the main theorems. The results are the sequential counterparts of some fixed sample size results derived in a concurrent paper of Sen, Bhattacharyya and Suh [9].
11 citations
01 Jan 1973
TL;DR: In this article, the results of Pyke on weak convergence of the empirical process with random sample size are simplified and extended to the case of p(>1)-dimensional stochastic vectors.
Abstract: : By the use of a semi-martingale property of the Kolmogorov supremum, the results of Pyke on the weak convergence of the empirical process with random sample size are simplified and extended to the case of p(>1)-dimensional stochastic vectors.
8 citations
TL;DR: For a fixed total sample size, a multistage procedure based on generalized U -statistics is developed for choosing a partition of this sample size into individual sample size for which the generalized variance of the estimator of the parameter vector is asymptotically minimized.
7 citations
TL;DR: In this article, the authors extend the simultaneous confidence intervals procedures (SCIP) along the lines of Chow and Robbins [3] and develop certain robust non-parametric SCIP based on the results of Sen [10] and Sen and Ghosh [11]; the allied efficiency results are also presented.
Abstract: The purpose of this paper is two-fold: (i) to extend the simultaneous confidence intervals procedures (SCIP) of Healy [7] along the lines of Chow and Robbins [3] and (ii) to develop certain robust non-parametric SCIP based on the results of Sen [10] and Sen and Ghosh [11]; the allied efficiency results are also presented.