Axiomatic development of profile likelihoods as the strength of evidence for composite hypotheses

作者：He Yanling; Huang Wenzheng; Liang Hua^*

来源：Communications in Statistics - Theory and Methods, 2007, 36(13-16): 2695-2706.

DOI：10.1080/03610920701386869

• composite hypotheses
• likelihood principle
• profile likelihoods
• statistical evidence
• the law of likelihood

One important type of question in statistical inference is how to interpret data as evidence. The law of likelihood provides a satisfactory answer in interpreting data as evidence for simple hypotheses, but remains silent for composite hypotheses. This article examines how the law of likelihood can be extended to composite hypotheses within the scope of the likelihood principle. From a system of axioms, we conclude that the strength of evidence for the composite hypotheses should be represented by an interval between lower and upper profiles likelihoods. This article is intended to reveal the connection between profile likelihoods and the law of likelihood under the likelihood principle rather than argue in favor of the use of profile likelihoods in addressing general questions of statistical inference. The interpretation of the result is also discussed.

• 出版日期2007
• 单位宜春学院