## Estimation of a symmetric distribution.(English)Zbl 0594.62015

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
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