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Semiparametric Efficient and Robust Estimation of an Unknown Symmetric Population Under Arbitrary Sample Selection Bias

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  • Yanyuan Ma
  • Mijeong Kim
  • Marc G. Genton

Abstract

We propose semiparametric methods to estimate the center and shape of a symmetric population when a representative sample of the population is unavailable due to selection bias. We allow an arbitrary sample selection mechanism determined by the data collection procedure, and we do not impose any parametric form on the population distribution. Under this general framework, we construct a family of consistent estimators of the center that is robust to population model misspecification, and we identify the efficient member that reaches the minimum possible estimation variance. The asymptotic properties and finite sample performance of the estimation and inference procedures are illustrated through theoretical analysis and simulations. A data example is also provided to illustrate the usefulness of the methods in practice.

Suggested Citation

  • Yanyuan Ma & Mijeong Kim & Marc G. Genton, 2013. "Semiparametric Efficient and Robust Estimation of an Unknown Symmetric Population Under Arbitrary Sample Selection Bias," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1090-1104, September.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:1090-1104
    DOI: 10.1080/01621459.2013.816184
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    References listed on IDEAS

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    1. A. Colin Cameron & Pravin K. Trivedi, 2010. "Microeconometrics Using Stata, Revised Edition," Stata Press books, StataCorp LP, number musr, March.
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    Cited by:

    1. Wang Miao & Peng Ding & Zhi Geng, 2016. "Identifiability of Normal and Normal Mixture Models with Nonignorable Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1673-1683, October.
    2. Laura Borrajo & Ricardo Cao, 2021. "Nonparametric estimation for big-but-biased data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 861-883, December.
    3. Mikhail Zhelonkin & Marc G. Genton & Elvezio Ronchetti, 2016. "Robust inference in sample selection models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 805-827, September.

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