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Penalized empirical likelihood estimation of semiparametric models

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  • Otsu, Taisuke

Abstract

We propose an empirical likelihood-based estimation method for conditional estimating equations containing unknown functions, which can be applied for various semiparametric models. The proposed method is based on the methods of conditional empirical likelihood and penalization. Thus, our estimator is called the penalized empirical likelihood (PEL) estimator. For the whole parameter including infinite-dimensional unknown functions, we derive the consistency and a convergence rate of the PEL estimator. Furthermore, for the finite-dimensional parametric component, we show the asymptotic normality and efficiency of the PEL estimator. We illustrate the theory by three examples. Simulation results show reasonable finite sample properties of our estimator.

Suggested Citation

  • Otsu, Taisuke, 2007. "Penalized empirical likelihood estimation of semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1923-1954, November.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:10:p:1923-1954
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. Jian Zhang, 2003. "Sieve Empirical Likelihood and Extensions of the Generalized Least Squares," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 1-24.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    5. Xihong Lin, 2004. "Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data," Biometrika, Biometrika Trust, vol. 91(1), pages 177-193, March.
    6. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    7. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    8. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    9. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, vol. 93(1), pages 75-84, March.
    10. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    11. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
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    Citations

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    Cited by:

    1. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
    2. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    3. Chunrong Ai & Xiaohong Chen, 2009. "Semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," CeMMAP working papers CWP28/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Xianyang Zhang & Xiaofeng Shao, 2016. "On the coverage bound problem of empirical likelihood methods for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 395-421, March.

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