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Semiparametric Regression Analysis under Imputation for Missing Response Data

Author

Listed:
  • Wolfgang Haerdle
  • Oliver Linton
  • Qihua Wang
Abstract
We develop inference tools in a semiparametric regression model with missing response data. A semiparametric regression imputation estimator, a marginal average estimator and a (marginal) propensity score weighted estimator are defined. All the estimators are proved to be asymptotically normal, with the same asymptotic variance. They achieve the semiparametric efficiency bound in the homoskedastic Gaussian case. We show that the Jackknife method can be used to consistently estimate the asymptotic variance. Our model and estimators are defined with a view to avoid the curse of dimensionality, and that severely limits the applicability of existing methods. The empirical likelihood method is developed. It is shown that when missing responses are imputed using the semiparametric regression method the empirical log-likelihood is asymptotically a scaled chi-square variable. An adjusted empirical log-likelihood ratio, which is asymptotically standard chi-square, is obtained. Also, a bootstrap empirical log-likelihood ratio is derived and its distribution is used to approximate that of the imputed empirical log-likelihood ratio. A simulation study is conducted to compare the adjusted and bootstrap empirical likelihood with the normal approximation-based method in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparison is also made by simulation between the proposed estimators and the related estimators. Furthermore, a real data analysis is given to illustrate our methods.

Suggested Citation

  • Wolfgang Haerdle & Oliver Linton & Qihua Wang, 2003. "Semiparametric Regression Analysis under Imputation for Missing Response Data," STICERD - Econometrics Paper Series 454, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:454
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    File URL: https://sticerd.lse.ac.uk/dps/em/em454.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Asymptotic normality; empirical likelihood; semiparametric imputation.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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