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Sufficiency, Prediction and Extreme Models

Steffen L. Lauritzen
Scandinavian Journal of Statistics
Vol. 1, No. 3 (1974), pp. 128-134
Stable URL: http://www.jstor.org/stable/4615564
Page Count: 7
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Sufficiency, Prediction and Extreme Models
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Abstract

A modified concept of sufficiency, relevant in connection with statistical analysis of stochastic processes, is defined and its basic properties investigated. A method of prediction that applies when the probability structure is partly unknown is introduced and the method is shown to possess certain important invariance properties. The concept of an extreme model is defined and its probabilistic and statistical properties discussed. Existence of maximum likelihood estimators and predictors is established under weak regularity assumptions. For technical convenience, only discrete-valued stochastic processes are considered throughout the paper.

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