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Relative deficiency of kernel type estimators of quantiles. (English) Zbl 0533.62040
Summary: 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.

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
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