The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association

Nour-Eddine Berrahou (), Salim Bouzebda () and Lahcen Douge ()
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Nour-Eddine Berrahou: University Cadi Ayyad
Salim Bouzebda: Université de technologie de Compiègne
Lahcen Douge: University Cadi Ayyad

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 2, 1-37

Abstract: 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.

Keywords: Bahadur-Kiefer representation; Sample quantiles; Empirical process; Bernstein polynomials; Q-Q plot; 60E05; 60F15; 62E15; 62G05; 62G20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11009-024-10086-x

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