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Note on multidimensional empirical processes for [phi]-mixing random vectors

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  • Yoshihara, Ken-ichi

Abstract

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.

Suggested Citation

  • Yoshihara, Ken-ichi, 1978. "Note on multidimensional empirical processes for [phi]-mixing random vectors," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 584-588, December.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:4:p:584-588
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