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Weak convergence in Lp(0,1) of the uniform empirical process under dependence

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  • Oliveira, P. E.
  • Suquet, Ch.

Abstract

The weak convergence of the empirical process of strong mixing or associated random variables is studied in LP(0,1). We find minimal rates of convergence to zero of the mixing coefficients or the covariances, in either case, supposing stationarity of the underlying variables. The rates obtained improve, for p not too large, the corresponding results in the classical D(0,1) framework.

Suggested Citation

  • Oliveira, P. E. & Suquet, Ch., 1998. "Weak convergence in Lp(0,1) of the uniform empirical process under dependence," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 363-370, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:4:p:363-370
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    References listed on IDEAS

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    1. Cremers, Heinz & Kadelka, Dieter, 1986. "On weak convergence of integral functionals of stochastic processes with applications to processes taking paths in LEP," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 305-317, February.
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    Cited by:

    1. Jean‐Marc Bardet & Paul Doukhan & José Rafael León, 2008. "Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 906-945, September.

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