Best equivariant nonparametric estimator of a quantile

Ryszard Zielinski

Statistics & Probability Letters, 1999, vol. 45, issue 1, 79-84

Abstract: Given q[set membership, variant](0,1) and a sample X1,X2,...,Xn from an unknown , an estimator T*=T*(X1,X2,...,Xn) of the qth quantile of the distribution F is constructed such that EFF(T*)-q[less-than-or-equals, slant]EFF(T)-q for all and for all , where is a non-parametric family of distributions and is a class of estimators. It is shown that T*=Xj:n for a suitably chosen jth order statistic. The best median-unbiased estimator is also constructed.

Keywords: Quantile; estimators; Nonparametric; model; Optimal; estimation; Equivariant; estimators; MAD; Median-unbiased; estimator (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (2)

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