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An empirical Bayes estimation problem.

H Robbins1

  • 1Columbia University, New York, New York 10027.

Proceedings of the National Academy of Sciences of the United States of America
|December 1, 1980
PubMed
Summary
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This study addresses estimating a parameter in statistical models with unknown prior distributions. Combining two estimation methods offers a consistent and efficient solution for large sample sizes.

Area of Science:

  • Statistics
  • Statistical Modeling
  • Bayesian Inference

Background:

  • Estimating parameters in statistical models with unknown prior distributions is challenging.
  • Traditional methods may lack consistency or efficiency depending on the prior's form.

Purpose of the Study:

  • To develop a robust estimation method for the parameter E(thetax = a) when the prior distribution G is unknown.
  • To resolve the dilemma between consistency and efficiency in parameter estimation.

Main Methods:

  • The study compares a Gamma prior assumption with a general empirical Bayes estimator.
  • A novel approach combines these two methods to leverage their respective strengths.

Main Results:

  • Assuming a Gamma prior provides a straightforward estimate but may lack consistency if the prior is misspecified.

Related Experiment Videos

  • Empirical Bayes estimators are consistent but can be inefficient if the prior is indeed Gamma.
  • Combining both methods offers a resolution, achieving both consistency and efficiency for large samples.

    • Conclusions:

    • A combined estimation strategy effectively addresses the limitations of individual methods.
    • This approach provides a more reliable parameter estimate in situations with unknown prior distributions, particularly for large datasets.