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Distance between nonidentically weakly dependent random vectors and Gaussian random vectors under the bounded Lipschitz metric

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  • Sancetta, Alessio

Abstract

This paper provides bounds for the rate of weak convergence of a multivariate weakly dependent nonidentically distributed partial sum to the Gaussian law. Using the approach of Bentkus [2003, On normal approximations, approximations of semigroups of operators, and approximations by accompanying laws. Available at the following URL: http://www.mathematik.uni-bielefeld.de/fgweb/Preprints/fg03035.pdf], we give an equivalent bound in terms of dimension, as in the case of iid random variables. The bound is stated in terms of minimal high-level assumptions.

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  • Sancetta, Alessio, 2005. "Distance between nonidentically weakly dependent random vectors and Gaussian random vectors under the bounded Lipschitz metric," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 158-168, December.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:3:p:158-168
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    References listed on IDEAS

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    1. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    2. Rüschendorf, Ludger & de Valk, Vincent, 1993. "On regression representations of stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 183-198, June.
    3. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
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