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Empirical likelihood for single-index models

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  • Xue, Liu-Gen
  • Zhu, Lixing

Abstract

The empirical likelihood method is especially useful for constructing confidence intervals or regions of the parameter of interest. This method has been extensively applied to linear regression and generalized linear regression models. In this paper, the empirical likelihood method for single-index regression models is studied. An estimated empirical log-likelihood approach to construct the confidence region of the regression parameter is developed. An adjusted empirical log-likelihood ratio is proved to be asymptotically standard chi-square. A simulation study indicates that compared with a normal approximation-based approach, the proposed method described herein works better in terms of coverage probabilities and areas (lengths) of confidence regions (intervals).

Suggested Citation

  • Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1295-1312
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    References listed on IDEAS

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    1. Qi-Hua Wang & Bing-Yi Jing, 2001. "Empirical Likelihood for a Class of Functionals of Survival Distribution with Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 517-527, September.
    2. Qin, Gengsheng & Jing, Bing-Yi, 2001. "Censored Partial Linear Models and Empirical Likelihood," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 37-61, July.
    3. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    4. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    5. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    6. Qihua Wang & J. N. K. Rao, 2002. "Empirical Likelihood‐based Inference in Linear Models with Missing Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 563-576, September.
    7. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    8. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
    9. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    10. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
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