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Rates of convergence in the central limit theorem for linear statistics of martingale differences

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  • Dedecker, Jérôme
  • Merlevède, Florence

Abstract

In this paper, we give rates of convergence for minimal distances between linear statistics of martingale differences and the limiting Gaussian distribution. In particular the results apply to the partial sums of (possibly long range dependent) linear processes, and to the least squares estimator in some parametric regression models.

Suggested Citation

  • Dedecker, Jérôme & Merlevède, Florence, 2011. "Rates of convergence in the central limit theorem for linear statistics of martingale differences," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1013-1043, May.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:5:p:1013-1043
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    References listed on IDEAS

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    1. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(1), pages 3-22, February.
    2. Volný, Dalibor, 1993. "Approximating martingales and the central limit theorem for strictly stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 41-74, January.
    3. Hannan, E. J., 1979. "The central limit theorem for time series regression," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 281-289, December.
    4. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
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