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Convergence of integrals of uniform empirical and quantile processes

Author

Listed:
  • Csörgo, Miklós
  • Horváth, Lajos
  • Shao, Qi-Man

Abstract

We find a necessary and sufficient condition for the weak convergence of the uniform empirical and quantile processes to a Brownian bridge in weighted Lp-distances. Under the same condition, weighted Lp-functionals of the uniform empirical and quantile processes converge in distribution to the corresponding functionals of a Brownian bridge. We also prove some dichotomy theorems for integrals of stochastic processes.

Suggested Citation

  • Csörgo, Miklós & Horváth, Lajos & Shao, Qi-Man, 1993. "Convergence of integrals of uniform empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 283-294, April.
    • Handle: RePEc:eee:spapps:v:45:y:1993:i:2:p:283-294
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    Citations

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    Cited by:

    1. Wenbo V. Li & Qi-Man Shao, 1999. "Small Ball Estimates for Gaussian Processes under Sobolev Type Norms," Journal of Theoretical Probability, Springer, vol. 12(3), pages 699-720, July.
    2. Qi-Man Shao, 2000. "A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 13(2), pages 343-356, April.
    3. Côté, Marie-Pier & Genest, Christian & Omelka, Marek, 2019. "Rank-based inference tools for copula regression, with property and casualty insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 1-15.
    4. Eustasio Barrio & Juan Cuesta-Albertos & Carlos Matrán & Sándor Csörgö & Carles Cuadras & Tertius Wet & Evarist Giné & Richard Lockhart & Axel Munk & Winfried Stute, 2000. "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 1-96, June.

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