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On the rate of approximation in the central limit theorem for dependent random variables and random vectors

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  • Basu, A. K.

Abstract

Large "O" and small "o" approximations of the expected value of a class of smooth functions (f [set membership, variant] Cr(R)) of the normalized partial sums of dependent random variable by the expectation of the corresponding functions of normal random variables have been established. The same types of approximations are also obtained for dependent random vectors. The technique used is the Lindberg-Lévy method generalized by Dvoretzky to dependent random variables.

Suggested Citation

  • Basu, A. K., 1980. "On the rate of approximation in the central limit theorem for dependent random variables and random vectors," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 565-578, December.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:4:p:565-578
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    Cited by:

    1. Dette, Holger & Derbort, Stephan, 2001. "Analysis of Variance in Nonparametric Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 110-137, January.
    2. Dung, Le Van & Son, Ta Cong, 2020. "On the rate of convergence in the central limit theorem for arrays of random vectors," Statistics & Probability Letters, Elsevier, vol. 158(C).

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