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Best equivariant nonparametric estimator of a quantile

Author

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  • Zielinski, Ryszard

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.

Suggested Citation

  • Zielinski, Ryszard, 1999. "Best equivariant nonparametric estimator of a quantile," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 79-84, October.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:1:p:79-84
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    References listed on IDEAS

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    1. Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
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    Cited by:

    1. Okolewski, Andrzej & Rychlik, Tomasz, 2001. "Sharp distribution-free bounds on the bias in estimating quantiles via order statistics," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 207-213, April.
    2. Malinovsky, Yaakov & Rinott, Yosef, 2009. "On stochastic orders of absolute value of order statistics in symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2086-2091, October.

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