Asymptotic Normality for a General Class of Statistical Functions and Applications to Measures of Spread

Abstract

A general class of statistical functionals is introduced and the asymptotic normality of the corresponding estimators is established. Included are certain measures of spread, proposed by Bickel and Lehmann (1979), for which the asymptotic distribution theory has been an open problem. The proofs involve some new results, of independent interest, for empirical and quantile processes.