A Berry-Esseen theorem for the kernel quantile estimator with application to studying the deficiency of quantile estimators |
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| Authors: | Xiaojing Xiang |
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| Institution: | (1) Department of Mathematics, University of Oregon, 97403 Eugene, OR, USA |
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| 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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| Keywords: | Berry-Esseen bound kernel quantile estimator sample quantile estimator deficiency |
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