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The Notion of Redundancy and Its Use as a Quantitative Measure of the Discrepancy between a Statistical Hypothesis and a Set of Observational Data [with Discussion]

Per Martin-Löf
Scandinavian Journal of Statistics
Vol. 1, No. 1 (1974), pp. 3-18
Stable URL: http://www.jstor.org/stable/4615544
Page Count: 16
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The Notion of Redundancy and Its Use as a Quantitative Measure of the Discrepancy between a Statistical Hypothesis and a Set of Observational Data [with Discussion]
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Abstract

It is proposed to supplement the critical level, as used in ordinary significance testing, by a measure of the magnitude of the departure of the observed set of data from the hypothesis to be tested. This measure, which is called the redundancy, appears in two versions, one microcanonical (or combinatorial) and the other canonical (or parametrical). The microcanomical redundancy is obtained by dividing minus the logarithm of the critical level by the Boltzmann entropy of the experiment and the canonical redundancy by dividing minus the logarithm of the likelihood ratio by the Gibbsian entropy. An approximation theorem shows that the former may be approximated asymptotically by the latter. The problem of calibrating the redundancy scale is discussed in connection with a series of examples, and, finally, certain considerations concerning the size of a statistical experiment are given which are based on the redundancy rather than the power function.

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