AN EXTENSION OF THE CSORGO-HORVATH FUNCTIONAL LIMIT-THEOREM AND ITS APPLICATIONS TO CHANGEPOINT PROBLEMS

[摘要] Consider a triangular array X(1)(n), ..., X(n)(n), n is an element of N, of rowwise independent random elements with values in a measurable space. Suppose there exists theta is an element of [0, 1)such that X(1)(n), ..., X([n theta])(n) have distribution nu(1) and X([n theta]+1)(n), ..., X(n)(n) have distribution nu(2). Csorgo and Horvath derived an invariance principle for a one-time parameter process, which is the foundation of a test for H-0:theta=0 versus H-1:theta is an element of(0, 1). We are interested in the more complex test problem (H) over tilde 0:theta is an element of Theta 0, versus (H) over tilde(1),:theta is not an element of Theta(0), where Theta(0) subset of or equal to(0, 1). To treat this new situation, we extend the Csorgo-Horvath result in proving a functional limit theorem for a suitable two-time parameter process. We briefly sketch several applications of our result. Especially, the power of the Csorgo-Horvath test is investigated in detail. (C) 1994 Academic Press, Inc.

[发布日期] 1994-11-01

[关键词] WEAK CONVERGENCE;MAXIMAL-INEQUALITIES;ASYMPTOTIC C-TIGHTNESS;APPLICATIONS TO CHANGEPOINT PROBLEMS