Abstract
A Berry-Esseen bound is established for the kernel quantile estimator under various conditions. The results improve an earlier result of Falk (1985,Ann. Statist.,13, 428–433) and rely on the local smoothness of the quantile function. This new Berry-Esseen bound is applied to studying the deficiency of the sample quantile estimator with respect to the kernel quantile estimator. A new result is obtained which is an extension of that in Falk (1985).
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Xiang, X. A Berry-Esseen theorem for the kernel quantile estimator with application to studying the deficiency of quantile estimators. Ann Inst Stat Math 47, 237–251 (1995). https://doi.org/10.1007/BF00773460
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DOI: https://doi.org/10.1007/BF00773460