Falk, Michael Relative deficiency of kernel type estimators of quantiles. (English) Zbl 0533.62040 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. Cited in 51 Documents 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 PDF BibTeX XML Cite \textit{M. Falk}, Ann. Stat. 12, 261--268 (1984; Zbl 0533.62040) Full Text: DOI OpenURL