Uniform and nonuniform estimates in the CLT for Banach valued dependent random variables

A. K. Basu

Journal of Multivariate Analysis, 1988, vol. 25, issue 2, 153-163

Abstract: A uniform estimate of the rate of convergence in the central limit theorem (CLT) in certain Banach spaces for dependent random variables is established when the Gaussian measure of the [epsilon]-neighbourhood of the boundary of a set is proportional to [epsilon] and the third order moment is finite in the strong sense. A uniform estimate in the CLT for Banach valued dependent random variables is carried out when the B-space is well behaved for a martingale transform.

Keywords: dependent; random; vector; B-valued; random; variable; central; limit; theorem; uniform; bound; nonuniform; bound; martingale; transform (search for similar items in EconPapers)
Date: 1988
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