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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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