This analysis demonstrates strong convergence rates and Berry–Esseen bounds in sample quantiles, indicating robust estimation techniques.
In this paper, we investigate the Bahadur representation for the linear kernel quantile estimator in the context of ANA random variables. The Bahadur representation is utilized to analyze the strong convergence rate of the linear kernel quantile estimator, as well as to establish its asymptotic normal properties and Berry–Esseen bounds under ANA random sequences. We employ the optimized Bahadur representation of the sample quantile under ANA random variables to accomplish this objective. Additionally, we conduct numerical simulations to further validate the theoretical results using finite samples, and we apply the estimation of sample quantiles and linear kernel quantiles to real data analysis.
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Yang et al. (2025) studied this question.
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