On some counter-counter-examples about classical inference

Benito Vittorio Frosini ()

Statistica, 2008, vol. 68, issue 2, 135-152

Abstract: This paper deals with theoretical concepts and practical examples, aimed at showing that non-Bayesian inference is liable to result in mistakes or unacceptable conclusions, and proves that they are not justified. Section 2 comments on examples when an objective prior distribution exists, and shows how widely one can be istaken in using a prior quite distant from the real one. Section 3 comments on two results by Godambe, stressing that in sampling from finite populations no flat likelihood exists, while an unbiased linear estimator with zero variance does not exist, unless we reach a complete knowledge of the population. Section 4 stresses the fundamental difference between a probability interval for a parameter, and a confidence interval aimed at making inference on the parameter, thus summarizing all certain facts and constraints able to shrink such an inferential interval. Section 5 explains why we are justified in attaching an inductive meaning to a realized confidence interval. Finally, Section 6 counters some well known counter-examples spread in the Bayesian literature, showing that they are unacceptable from a sound inductive basis.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:bot:rivsta:v:68:y:2008:i:2:p:135-152

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