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The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association

Author

Listed:
  • Nour-Eddine Berrahou

    (University Cadi Ayyad)

  • Salim Bouzebda

    (Université de technologie de Compiègne)

  • Lahcen Douge

    (University Cadi Ayyad)

Abstract

In this paper, the Bahadur representation of the empirical and Bernstein polynomials estimators of the quantile function based on associated sequences are investigated. The rate of approximation depends on the rate of decay in covariances, and it converges to the optimal rate observed under independence when the covariances quickly approach zero. As an application, we establish a Berry-Esseen bound with the rate $$O(n^{-1/3})$$ O ( n - 1 / 3 ) assuming polynomial decay of covariances. All these results are established under fairly general conditions on the underlying distributions. Additionally, we perform Monte Carlo simulations to evaluate the finite sample performance of the suggested estimators, utilizing an associated and non-mixing model.

Suggested Citation

  • Nour-Eddine Berrahou & Salim Bouzebda & Lahcen Douge, 2024. "The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-37, June.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:2:d:10.1007_s11009-024-10086-x
    DOI: 10.1007/s11009-024-10086-x
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