Note on multidimensional empirical processes for [phi]-mixing random vectors
In 1974, Sen proved weak convergence of the empirical processes (in the J1-topology on Dp[0, 1]) for a stationary [phi]-mixing sequence of stochastic p([greater, double equals] 1)-vectors. In this note, we show that Sen's theorem on weak convergence of the multidimensional empirical process for a stationary [phi]-mixing sequence of stochastic vectors remains true under a less restrictive condition on the mixing constants {[phi]n}, i.e., [phi]n = O(n-1-[delta]) for some [delta] > 0.
Year of publication: |
1978
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Authors: | Yoshihara, Ken-ichi |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 8.1978, 4, p. 584-588
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Publisher: |
Elsevier |
Subject: | Dp[0 | 1] space empirical processes Gaussian process [phi]-mixing Skorokhod J1-topology weak convergence |
Saved in:
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