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Rates of convergence for classes of functions: The non-i.i.d. case

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  • Yukich, J. E.

Abstract

Let Xi, i >= 1, be a sequence of [phi]-mixing random variables with values in a sample space (X, A). Let L(Xi) = P(i) for all i >= 1 and let n, n >= 1, be classes of real-valued measurable functions on (X, A). Given any function g on (X, A), let Sn(g) = [Sigma]i = 1n {g(Xi) - Eg(Xi)}. Under weak metric entropy conditions on n and under growth conditions on both the mixing coefficients and the maximal variance V := V(n) := maxi

Suggested Citation

  • Yukich, J. E., 1986. "Rates of convergence for classes of functions: The non-i.i.d. case," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 175-189, December.
    • Handle: RePEc:eee:jmvana:v:20:y:1986:i:2:p:175-189
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    Cited by:

    1. Richard Nickl & Benedikt M. Pötscher, 2007. "Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov- and Sobolev-Type," Journal of Theoretical Probability, Springer, vol. 20(2), pages 177-199, June.
    2. Magda Peligrad, 2001. "A Note on the Uniform Laws for Dependent Processes Via Coupling," Journal of Theoretical Probability, Springer, vol. 14(4), pages 979-988, October.
    3. Peligrad, Magda, 2002. "Some remarks on coupling of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 201-209, November.
    4. Donald W.K. Andrews & David Pollard, 1990. "A Functional Central Limit Theorem for Strong Mixing Stochastic Processes," Cowles Foundation Discussion Papers 951, Cowles Foundation for Research in Economics, Yale University.

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