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Asymptotic expansions in functional limit theorems

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  • Götze, F.

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.

Suggested Citation

  • Götze, F., 1985. "Asymptotic expansions in functional limit theorems," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 1-20, February.
    • Handle: RePEc:eee:jmvana:v:16:y:1985:i:1:p:1-20
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    Cited by:

    1. Miguel A. Delgado, 1996. "Testing Serial Independence Using The Sample Distribution Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(3), pages 271-285, May.

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