Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space

S.A. Bogatyrev, F. Götze and V.V. Ulyanov

Journal of Multivariate Analysis, 2006, vol. 97, issue 9, 2041-2056

Abstract: We consider short asymptotic expansions for the probability of a sum of i.i.d. random elements to hit a ball in a Hilbert space H. The error bound for the expansion is of order O(n-1). It depends on the first 12 eigenvalues of the covariance operator only. Moreover, the bound is non-uniform, i.e. the accuracy of the approximation becomes better as the distance between a boundary of the ball and the origin in H grows.

Keywords: Central; limit; theorem; Hilbert; space; Gaussian; approximation; Edgeworth; expansions; Covariance; operator (search for similar items in EconPapers)
Date: 2006
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