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Optimal pseudolikelihood estimation in the analysis of multivariate missing data with nonignorable nonresponse.

Jiwei Zhao1, Yanyuan Ma2

  • 1Department of Biostatistics, State University of New York at Buffalo, 719 Kimball Tower, Buffalo, New York, U.S.A.

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|February 26, 2019
PubMed
Summary

This study proves the nonparametric pseudolikelihood estimator is more efficient for regression models with nonignorable missing responses. The findings enhance understanding of missing data methods in statistical modeling.

Keywords:
EfficiencyMissing dataNonignorable nonresponsePseudolikelihood estimator

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Econometrics

Background:

  • Regression models with missing response data present challenges, particularly when missingness depends on the response itself (nonignorable).
  • Tang et al. (2003) introduced three pseudolikelihood estimators for such models, differing in how covariate distributions are handled.
  • Prior work established the efficiency of parametric estimation over a known covariate distribution but conjectured the superiority of nonparametric estimation.

Purpose of the Study:

  • To rigorously investigate the asymptotic behavior of the nonparametric pseudolikelihood estimator.
  • To mathematically prove the enhanced efficiency of the nonparametric estimator compared to existing methods.
  • To extend the applicability of these findings to broader classes of nonignorable missingness mechanisms.

Main Methods:

  • Derivation of a closed-form representation for the asymptotic variance of the nonparametric estimator.
  • Asymptotic analysis to establish the statistical efficiency bounds of the estimators.
  • Theoretical comparison of the proposed nonparametric estimator against parametric and known-distribution approaches.

Main Results:

  • A closed-form expression for the asymptotic variance of the third (nonparametric) estimator was successfully derived.
  • The nonparametric estimator was mathematically proven to be more efficient than the first two estimators (known covariate distribution and parametric estimation).
  • The theoretical framework supports the application of these results to more general missingness mechanisms.

Conclusions:

  • The nonparametric pseudolikelihood estimator offers superior efficiency for regression models with nonignorable missing responses.
  • This study provides theoretical validation for the conjecture regarding the nonparametric estimator's advantage.
  • The derived results offer a robust theoretical foundation for handling complex missing data scenarios in statistical analysis.