Weak Convergence of Sequential Linear Rank Statistics
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TLDR
In this paper, a Chernoff-Savage linear rank statistics is introduced as a basis for inference, and the principal result is an invariance principle for two-sample rank statistics, i.e., under a fixed alternative the sequence of sequential linear rank statistic converges weakly to a Wiener process.Abstract:
A sequential version of Chernoff-Savage linear rank statistics is introduced as a basis for inference. The principal result is an invariance principle for two-sample rank statistics, i.e., under a fixed alternative the sequence of sequential linear rank statistics converges weakly to a Wiener process. The domain of application of the theorem is quite broad and includes score functions which tend to infinity at the end points much more rapidly than that of the normal scores test. The method of proof involves new results in the theory of multiparameter empirical processes as well as some new probability bounds on the joint behavior of uniform order statistics. Applications of weak convergence are explored; in particular, the extension of the theory of Pitman efficiency to the sequential case.read more
Citations
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Convergence of Probability Measures
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Some invariance principles for mized rank statistics and induced order statistics and some application
TL;DR: The structural affinity of mixed rank statistics and linear combinations of functions of concomitants of order statistics (or induced order statistics) is examined in this paper, and some weal as well as strong invariance principles for these statistics are studied.
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Non-parametric sequential tests for symmetry
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References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Journal ArticleDOI
Convergence of Random Processes and Limit Theorems in Probability Theory
TL;DR: In this article, the convergence of stochastic processes is defined in terms of the so-called weak convergence of probability measures in appropriate functional spaces (c.m. s. s.).
Journal ArticleDOI
Limit Theorems for Stochastic Processes
TL;DR: The authors consider a sequence of processes such that the multivariate distribution of the processes of the process (i.e., the process of finding the distribution of a set of processes) tends to the multi-dimensional distribution of that process.
Journal ArticleDOI
Convergence Criteria for Multiparameter Stochastic Processes and Some Applications
P. J. Bickel,M. J. Wichura +1 more
TL;DR: In this paper, the authors derived thehentsov-Billingsley type fluctuation inequalities for stochastic processes whose time parameter ranges over the $q$-dimensional unit cube and established weak convergence results for such processes.