The almost sure invariance principles of degenerate U-statistics of degree two for stationary random variables

S. Kanagawa and K. Yoshihara

Stochastic Processes and their Applications, 1994, vol. 49, issue 2, 347-356

Abstract: The almost sure invariance principle for some degenerate U-statistics of degree two is considered for strictly stationary random variables satisfying mixing conditions. The error term obtained is O(t1 - [gamma]) which yields Donsker's and Strassen's invariance principles for the U-statistics. The approach used here is based upon Hoeffding's expansion of kernel functions and the almost sure invariance principles for partial sums of Banach space valued mixing random variables.

Keywords: almost; sure; invariance; principle; U-statistics; strongly; mixing; absolutely; regular; mixing; [phi]-mixing (search for similar items in EconPapers)
Date: 1994
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