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Related Experiment Videos

Sequential Estimation of p with Squared Relative Error Loss.

P Cabilio1, H Robbins

  • 1Acadia University, Wolfville, Nova Scotia.

Proceedings of the National Academy of Sciences of the United States of America
|January 1, 1975
PubMed
Summary
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This study develops a sequential estimation method for the probability of success (p) in Bernoulli trials. A new Bayes procedure improves accuracy, especially when p is close to 0 or 1, with a Bayes risk approaching 2π√c as observation cost c approaches 0.

Area of Science:

  • Statistics
  • Probability Theory
  • Sequential Analysis

Background:

  • Sequential estimation of probability 'p' in Bernoulli trials is crucial for various applications.
  • Traditional methods struggle with accuracy when 'p' approaches 0 or 1.
  • The symmetrized relative squared error loss is suitable for 'p' near boundary values.

Purpose of the Study:

  • To develop a robust sequential estimation procedure for 'p'.
  • To address the limitations of existing heuristic methods for extreme 'p' values.
  • To introduce and analyze a Bayes procedure using a uniform prior.

Main Methods:

  • Heuristic sequential sample size determination.
  • Terminal estimation of 'p'.
  • Introduction of a uniform prior distribution for 'p'.

Related Experiment Videos

  • Derivation and analysis of the Bayes procedure.

    • Main Results:

    • A heuristic procedure performs well for intermediate 'p' as cost 'c' approaches 0.
    • This heuristic fails for 'p' near 0 or 1 when 'c' is fixed.
    • The Bayes procedure with a uniform prior demonstrates improved performance for extreme 'p' values.
    • The Bayes risk for the new procedure approximates 2π√c as 'c' approaches 0.

    Conclusions:

    • The proposed Bayes procedure offers a significant improvement for sequential estimation of 'p', particularly in boundary cases.
    • The uniform prior is effective in mitigating issues with extreme probabilities.
    • The asymptotic Bayes risk provides a theoretical performance benchmark for the new method.