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Empirical likelihood confidence intervals for M-functionals in the presence of auxiliary information

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  • Zhang, Biao

Abstract

In this paper, we employ the method of empirical likelihood to construct confidence intervals for M-functionals in the presence of auxiliary information under a nonparametric setting. The modified empirical likelihood confidence intervals which make use of the knowledge of auxiliary information are asymptotically at least as narrow as the standard ones which do not utilize auxiliary information. For testing a hypothesis about a M-functional, the power of a test statistic based on the modified empirical likelihood ratio is larger than the one based on the standard empirical likelihood ratio. A simulation study is presented to demonstrate the performance of the modified empirical likelihood confidence intervals for small samples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:1:p:87-97
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    Cited by:

    1. Han-Ying Liang & Jacobo Uña-Álvarez, 2012. "Empirical likelihood for conditional quantile with left-truncated and dependent data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 765-790, August.
    2. 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.
    3. Wang, Qihua & Yu, Keming, 2007. "Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 455-480, March.

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