Estimation of a symmetric distribution. (English) Zbl 0594.62015

Lo, Shaw-Hwa

Ann. Stat. 13, 1097-1113 (1985).

The main result of this paper establishes the fact, that for a sequence \(X_ 1,...,X_ n\) of i.i.d. random variables with d.f. \(F(x)=F_ 0(x- \theta)\), \(F_ 0\) being symmetric at zero, the empirical d.f. symmetrized at some appropriate estimate of \(\theta\) is asymptotically minimax-efficient for F.

Reviewer: W.Stute

MSC:

62E20	Asymptotic distribution theory in statistics
62G20	Asymptotic properties of nonparametric inference
62G30	Order statistics; empirical distribution functions

Keywords:

empirical distribution function; symmetric distribution functions; Gaussian experiments; asymptotically minimax estimators; location