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

Ken-ichi Yoshihara

Journal of Multivariate Analysis, 1978, vol. 8, issue 4, 584-588

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.

Keywords: Dp[0; 1] space empirical processes Gaussian process [phi]-mixing Skorokhod J1-topology weak convergence (search for similar items in EconPapers)
Date: 1978
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