Testing Statistical Hypotheses pp 3-27 | Cite as

# The General Decision Problem

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.

## Keywords

Loss Function Decision Problem Conditional Distribution Decision Procedure Risk Function## Preview

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