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An Information Criterion for Auxiliary Variable Selection in Incomplete Data Analysis.

Shinpei Imori1,2, Hidetoshi Shimodaira3,2

  • 1Graduate School of Science, Hiroshima University, Hiroshima 739-8526, Japan.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This study introduces a new information criterion to select relevant auxiliary variables for statistical inference with incomplete primary data. This method improves prediction accuracy by leveraging closely related auxiliary information.

Keywords:
Akaike information criterionFisher information matrixKullback–Leibler divergenceTakeuchi information criterionauxiliary variablesincomplete datamisspecification

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Area of Science:

  • Statistics
  • Data Science
  • Econometrics

Background:

  • Statistical inference often involves primary variables with some missing observations.
  • Auxiliary variables can enhance primary variable estimation if related, but hinder it if irrelevant.

Purpose of the Study:

  • To develop a method for selecting useful auxiliary variables in incomplete data analysis.
  • To propose an information criterion for predicting primary variables using auxiliary information.

Main Methods:

  • Formulating auxiliary variable selection as a model selection problem.
  • Proposing a novel information criterion as an asymptotically unbiased estimator of Kullback-Leibler divergence.
  • Establishing asymptotic equivalence with leave-one-out cross-validation.

Main Results:

  • The proposed information criterion effectively selects relevant auxiliary variables.
  • The method demonstrates improved estimation accuracy in the presence of incomplete primary data.
  • Performance validated through simulation and real-world data analysis.

Conclusions:

  • The developed information criterion offers a robust approach for auxiliary variable selection in incomplete data settings.
  • This method enhances the reliability of statistical inference by optimally utilizing auxiliary information.