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Empirical likelihood for single-index models

Author

Listed:
  • 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. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
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