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

Falk, Michael

Ann. Stat. 12, 261-268 (1984).

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.

MSC:

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

Keywords:

kernel type estimators of quantiles; mean square errors of estimators; Bahadur approximation; asymptotic relative deficiency; sample q-quantile