Asymptotic normality for a general class of statistical functions and applications to measures of spread. (English) Zbl 0554.62014

Janssen, Paul; Serfling, Robert; Veraverbeke, Noël

Ann. Stat. 12, 1369-1379 (1984).

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 P. J. Bickel and E. L. Lehmann [Contributions to statistics, Jaroslav Hájek Mem. Vol., 33-40 (1979; Zbl 0415.62015)], 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.

MSC:

62E20	Asymptotic distribution theory in statistics
62G05	Nonparametric estimation
60F05	Central limit and other weak theorems

Keywords:

differentiable statistical functionals; empirical processes; U-statistics structure; robustness; generalized L-functionals; asymptotic normality; measures of spread; quantile processes

Citations:

Zbl 0415.62015