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

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  • Basu, A. K.

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.

Suggested Citation

  • Basu, A. K., 1988. "Uniform and nonuniform estimates in the CLT for Banach valued dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 153-163, May.
    • Handle: RePEc:eee:jmvana:v:25:y:1988:i:2:p:153-163
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    Cited by:

    1. Kundu, Subrata & Majumdar, Suman & Mukherjee, Kanchan, 2000. "Central Limit Theorems revisited," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 265-275, April.

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