## ::Statistical theory

### ::concepts

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The **theory of statistics** provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics.<ref>Cox & Hinkley (1974, p.1)</ref><ref name="RaoOpt">
{{#invoke:citation/CS1|citation
|CitationClass=book
}}</ref> The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures.<ref name="RaoOpt"/><ref>Lehmann & Romano (2005)</ref>

Apart from philosophical considerations about how to make statistical inferences and decisions, much of statistical theory consists of mathematical statistics, and is closely linked to probability theory, to utility theory, and to optimization.

**Statistical theory sections**

Intro Scope See also Notes References Further reading

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