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Weighted empirical likelihood inference

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  • Wu, Changbao

Abstract

A weighted empirical likelihood approach is proposed to take account of the heteroscedastic structure of the data. The resulting weighted empirical likelihood ratio statistic is shown to have a limiting chisquare distribution. A limited simulation study shows that the associated confidence intervals for a population mean or a regression coefficient have more accurate coverage probabilities and more balanced two-sided tail errors when the sample size is small or moderate. The proposed weighted empirical likelihood method also provides more efficient point estimators for a population mean in the presence of side information. Large sample resemblances between the weighted and the unweighted empirical likelihood estimators are characterized through high-order asymptotics and small sample discrepancies of these estimators are investigated through simulation. The proposed weighted approach reduces to the usual unweighted empirical likelihood method under a homogeneous variance structure.

Suggested Citation

  • Wu, Changbao, 2004. "Weighted empirical likelihood inference," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 67-79, January.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:1:p:67-79
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    Citations

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    Cited by:

    1. Yongsong Qin, 2021. "Empirical Likelihood for Spatial Autoregressive Models with Spatial Autoregressive Disturbances," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 1-25, February.
    2. Bedoui, Adel & Lazar, Nicole A., 2020. "Bayesian empirical likelihood for ridge and lasso regressions," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    3. Sang, Peijun & Wang, Liangliang & Cao, Jiguo, 2019. "Weighted empirical likelihood inference for dynamical correlations," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 194-206.
    4. Yongsong Qin & Qingzhu Lei, 2021. "Empirical Likelihood for Mixed Regressive, Spatial Autoregressive Model Based on GMM," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 353-378, February.
    5. Yongli Sang & Xin Dang & Yichuan Zhao, 2020. "Depth-based weighted jackknife empirical likelihood for non-smooth U-structure equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 573-598, June.

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