Conditional Confidence Statements and Confidence Estimators

Abstract

Procedures are given for assessing the conclusiveness of a decision in terms of a (chance) conditional confidence coefficient Γ that has frequentist interpretability analogous to that of a traditional confidence coefficient. Properties of such procedures are compared in terms of the distribution of Γ. This leads to recommendations on the choice of conditioning. Also, a methodology for estimating the confidence when it depends on unknown parameter values is given. The notions of confidence are not limited to interval estimation; examples are also given in hypothesis testing and selection problems and in nonparametric and sequential settings.

Key Words:

• Conditional confidence
• Estimated confidence
• Conditioning partition
• Ancillarity
• Estimated risk
• Hypothesis testing
• Interval estimation
• Selection and ranking
• Nonparametric procedures
• Sequential procedures