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A projection type distribution function and quantile estimates in the presence of auxiliary information

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  • Hengjian, Cui

Abstract

The strong consistency, asymptotic normality and the law of the iterated logarithm of a projection type distribution function and quantile estimates in the presence of the auxiliary information Eg(X)=0 are obtained by using the empirical likelihood method. The Bahadur representation of a projection type quantile estimate is also given. Moreover, their asymptotic variances are smaller than that of classical distribution and quantile estimates, respectively.

Suggested Citation

  • Hengjian, Cui, 2000. "A projection type distribution function and quantile estimates in the presence of auxiliary information," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 91-100, May.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:1:p:91-100
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    References listed on IDEAS

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    1. Zhang, Biao, 1997. "Empirical likelihood confidence intervals for M-functionals in the presence of auxiliary information," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 87-97, February.
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