Asymptotic expansions in functional limit theorems

F. Götze

Journal of Multivariate Analysis, 1985, vol. 16, issue 1, 1-20

Abstract: Asymptotic expansions for a class of functional limit theorems are investigated. It is shown that the expansions in this class fit into a common scheme, defined by a sequence of functions hn ([var epsilon]1,..., [var epsilon]n), n >= 1, of "weights" (for nobservations), which are smooth, symmetric, compatible and have vanishing first derivatives at zero. Then hn(n-1/2,..., n-1/2) admits an asymptotic expansion in powers of n-1/2. Applications to quadratic von Mises functionals, the C.L.T. in Banach spaces, and the invariance principle are discussed.

Keywords: Functional; limit; theorems; central; limit; theorem; Edgeworth; expansions; invariance; principle; empirical; process (search for similar items in EconPapers)
Date: 1985
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