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February, 1976 A Two-Dimensional Functional Permutational Central Limit Theorem for Linear Rank Statistics
Pranab Kumar Sen
Ann. Probab. 4(1): 13-26 (February, 1976). DOI: 10.1214/aop/1176996177

Abstract

Some two-dimensional time-parameter stochastic processes are constructed from a sequence of linear rank statistics by considering their projections on the spaces generated by the (double) sequence of anti-ranks. Under appropriate regularity conditions, it is shown that these processes weakly converge to Brownian sheets in the Skorokhod $J_1$-topology on the $D^2\lbrack 0, 1 \rbrack$ space. This unifies and extends earlier one-dimensional invariance principles for linear rank statistics to the two-dimensional case. The case of contiguous alternatives is treated briefly.

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Pranab Kumar Sen. "A Two-Dimensional Functional Permutational Central Limit Theorem for Linear Rank Statistics." Ann. Probab. 4 (1) 13 - 26, February, 1976. https://doi.org/10.1214/aop/1176996177

Information

Published: February, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0338.60008
MathSciNet: MR394793
Digital Object Identifier: 10.1214/aop/1176996177

Subjects:
Primary: 60B10
Secondary: 60F05 , 62G99

Keywords: $D^2\lbrack 0, 1 \rbrack$ space , $J_1$-topology , Brownian sheet , contiguity , Linear rank statistics , permutational central limit theorems , tightness , two-dimensional stochastic processes and weak convergence

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 1 • February, 1976
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