Minimax Stopping Rules When the Underlying Distribution is Uniform

Abstract

An invariance-based method of obtaining the minimax stopping rule when sampling from an unknown uniform distribution is presented and applied to two problems, maximizing the probability of selecting the smallest observation and minimizing the expected quantile of the observation selected. In the first problem the minimax rules use only the relative ranks of the observations; in the second they are shown to achieve asymptotic risk. Except for a few small values of the sample size the minimax rules are the formal Bayes rules with respect to an improper a priori 'density' whose a posteriori density given the first two observations is proper.

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Document Details

Document Type
Technical Report
Publication Date
Oct 25, 1979
Accession Number
ADA080387

Entities

People

  • Stephen M. Samuels

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Data Science
  • Equations
  • Identities
  • Inequalities
  • Invariance
  • Mathematics
  • Military Research
  • Probability
  • Random Variables
  • Sampling
  • Security
  • Statistical Algorithms
  • Statistics
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Statistical inference.