A generalized quantile estimator

Abstract

An alternative to the conventional sample quantlle Is proposed as a nonparametrlc estimator of a continuous population quantlle.The alternative estimator Is a "generalized sample quantlle" obtained by averaging an appropriate subsample quantlle over all subsamples of .a fixed size.Since the resulting statistic is a U-statistic with representation also as a linear combination of order statistics, known results are employed then to establish asymptotic normality.The alternative estimator is shown to be asymptotically efficient in the class of nonparametrlc models specified by Pfanzagl (1975).Analytic results and Monte Carlo studies with a moderate sample size for a variety of distributions Indicate that the proposed estimator usually provides mean square error of estimation less than that of the conventional sample quantile.

Keywords:

• order statistics
• sample quant He
• L estimator
• U-statistics
• U-statistics
• mean square error
• robust
• asymptotic normality