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February, 1974 Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes
Pranab Kumar Sen
Ann. Probab. 2(1): 147-154 (February, 1974). DOI: 10.1214/aop/1176996760

Abstract

For a stationary $\phi$-mixing sequence of stochastic $p(\geqq 1)$-vectors, weak convergence of the empirical process (in the $J_1$-topology on $D^p\lbrack 0, 1 \rbrack)$ to an appropriate Gaussian process is established under a simple condition on the mixing constants $\{\phi_n\}$. Weak convergence for random number of stochastic vectors is also studied. Tail probability inequalities for Kolmogorov Smirnov statistics are provided.

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Pranab Kumar Sen. "Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes." Ann. Probab. 2 (1) 147 - 154, February, 1974. https://doi.org/10.1214/aop/1176996760

Information

Published: February, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0276.60030
MathSciNet: MR402845
Digital Object Identifier: 10.1214/aop/1176996760

Subjects:
Primary: 60F05
Secondary: 60B10

Keywords: $D^p \lbrack 0, 1 \rbrack$ space , Empirical processes , Gaussian process , random sample size , Skorokhod $J_1$-topology , tightness , weak convergence

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 1 • February, 1974
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