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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 98 (2007)
Issue (Month): 10 (November)
Pages: 1923-1954

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Handle: RePEc:eee:jmvana:v:98:y:2007:i:10:p:1923-1954

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Keywords: Semiparametric model Empirical likelihood Penalization;

References

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  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  2. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, Econometric Society, vol. 72(6), pages 1667-1714, November.
  3. Newey, W.K., 1989. "Efficient Instrumental Variables Estimation Of Nonlinear Models," Papers, Princeton, Department of Economics - Econometric Research Program 341, Princeton, Department of Economics - Econometric Research Program.
  4. 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.
  5. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, Biometrika Trust, vol. 93(1), pages 75-84, March.
  6. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 72(1), pages 132-148, January.
  7. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, Econometric Society, vol. 71(6), pages 1795-1843, November.
  9. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, 9.
  10. Xihong Lin, 2004. "Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data," Biometrika, Biometrika Trust, Biometrika Trust, vol. 91(1), pages 177-193, March.
  11. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, 9.
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Cited by:
  1. Chunrong Ai & Xiaohong Chen, 2009. "Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1731, Cowles Foundation for Research in Economics, Yale University.

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