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Semiparametric estimation for inverse density weighted expectations when responses are missing at random

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  • Xuewen Lu
  • Heng Lian
  • Wanrong Liu

Abstract

When responses are missing at random, we consider semiparametric estimation of inverse density weighted expectations, or equivalently, integrals of conditional expectations. An inverse probability weighted estimator and a full propensity score weighted estimator are proposed and shown to be asymptotically normal. The two estimators are asymptotically equivalent and achieve the semiparametric efficiency bound. The performances of the estimators are investigated and compared with simulation studies and a real data example.

Suggested Citation

  • Xuewen Lu & Heng Lian & Wanrong Liu, 2012. "Semiparametric estimation for inverse density weighted expectations when responses are missing at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 139-152.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:139-152
    DOI: 10.1080/10485252.2011.599385
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    References listed on IDEAS

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    1. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    2. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    3. Lewbel, Arthur & Schennach, Susanne M., 2007. "A simple ordered data estimator for inverse density weighted expectations," Journal of Econometrics, Elsevier, vol. 136(1), pages 189-211, January.
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