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Empirical Likelihood for Estimating Equations with Nonignorably Missing Data.

Niansheng Tang1, Puying Zhao1, Hongtu Zhu2

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Summary
This summary is machine-generated.

This study introduces empirical likelihood (EL) inference for generalized estimating equations with missing data. The new method improves statistical efficiency and parameter estimation accuracy using kernel regression imputation.

Keywords:
Empirical likelihoodestimating equationsexponential tiltingimputationkernel regressionnonignorable missing data

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Missing data in generalized estimating equations (GEE) pose challenges for parameter inference.
  • Nonignorable missingness requires specialized methods beyond standard GEE.
  • Empirical likelihood (EL) offers a robust framework for statistical inference.

Purpose of the Study:

  • To develop empirical likelihood (EL) inference for parameters in generalized estimating equations (GEE) with nonignorably missing response data.
  • To propose a novel imputation method using kernel regression for handling missing data within the EL framework.
  • To evaluate the statistical efficiency and finite sample performance of the proposed EL estimators.

Main Methods:

  • Utilizing an exponential tilting model to characterize the nonignorably missing mechanism.
  • Modifying estimating equations by imputing missing data via kernel regression.
  • Establishing asymptotic properties of the empirical likelihood estimators under various scenarios.
  • Employing simulation studies to assess finite sample performance.

Main Results:

  • The proposed empirical likelihood estimators demonstrate statistical efficiency, especially when auxiliary information is available.
  • Asymptotic properties of the EL estimators are established, providing theoretical justification.
  • Simulation studies confirm the reliable finite sample performance of the developed method.
  • The method is successfully applied to analyze earnings data from the New York Social Indicators Survey.

Conclusions:

  • The developed empirical likelihood inference provides a statistically efficient and robust method for analyzing generalized estimating equations with nonignorably missing data.
  • The kernel regression imputation technique effectively addresses missing data, enhancing parameter estimation.
  • The findings offer a valuable tool for researchers dealing with complex missing data problems in various scientific fields.