Rationality and Unbiasedness in Hypothesis Testing

Abstract

The notion of a “rationality criterion” is defined. This criterion reflects a desirable property for statistical procedures that deal with censored data. In hypothesis testing situations, we show that when adapting this criterion to a uniformly most powerful unbiased (UMPU) test of comparing the scale parameters of two distributions, sometimes it is possible to determine a test so that it is unbiased and sometimes this is impossible. The question thus remains: What is more “rational”—the “rationality criterion” or unbiasedness?

Key Words:

• Censoring principle
• Likelihood principle
• Neyman-Pearsonian inference
• Type I censoring
• Unbiased testing