The raw material of a statistical investigation is a set of observations; these are the values taken on by random variables X whose distribution P θ is at least partly unknown. Of the parameter θ, which labels the distribution, it is assumed known only that it lies in a certain set Ω, the parameter space. Statistical inference is concerned with methods of using this observational material to obtain information concerning the distribution of X or the parameter θ with which it is labeled. To arrive at a more precise formulation of the problem we shall consider the purpose of the inference.
The above discussion suggests that the aim of statistics is the selection of a decision function which minimizes the resulting risk. As will be seen later, this statement of aims is not sufficiently precise to be meaningful; its proper interpretation is in fact one of the basic problems of the theory. The above discussion suggests that the aim of statistics is the selection of a decision function which minimizes the resulting risk. As will be seen later, this statement of aims is not sufficiently precise to be meaningful; its proper interpretation is in fact one of the basic problems of the theory.
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© 2005 Springer Science+Business Media, LLC
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(2005). The General Decision Problem. In: Testing Statistical Hypotheses. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/0-387-27605-X_1
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