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Statistical evidence in experiments and in record values. (English) Zbl 1105.62005

Summary: According to the law of likelihood, statistical evidence for one (simple) hypothesis against another is measured by the likelihood ratio. When the experimenter can choose between two or more experiments (of approximately the same cost) to obtain data, he would want to know which experiment provides (on average) stronger true evidence for one hypothesis against another. In this article, after defining a pre-experimental criterion for the potential strength of evidence provided by an experiment, based on entropy distance, we compare the potential statistical evidence in lower record values with that in the same number of iid observations from the same parent distribution. We also establish a relation between Fisher information and Kullback-Leibler distance.

MSC:

62B15 Theory of statistical experiments
62G32 Statistics of extreme values; tail inference
62B10 Statistical aspects of information-theoretic topics
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[1] DOI: 10.1007/s001840000089 · Zbl 0990.62044 · doi:10.1007/s001840000089
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