Relative Deficiency of Kernel Type Estimators of Quantiles
Open Access
- 1 March 1984
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 12 (1) , 261-268
- https://doi.org/10.1214/aos/1176346405
Abstract
In this paper the asymptotic relative deficiency of the sample $q$-quantile with respect to kernel type estimators of the $q$-quantile is evaluated. The comparison is based on the mean square errors of the estimators. The result suggests a purely analytic measure of performance within the class of kernels. It is notable that a similar situation occurs when kernel estimators of a distribution function are studied.Keywords
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