# Statistical Theory

A Statistical Theory is a Mathematical Theory that analyses and extends a statistical model family.

**Context:**- It can be extended by Statistics Research.
- It can be applied to some Task by an Applied Statistician.
- It can often be a reference to Probability Theory.

**Example(s):****Counter-Example(s):**.**See:**Statistics Academic Discipline, Mathematical Optimization, Study Design, Data Analysis, Statistical Decision Theory, Statistical Inference, Mathematical Statistics, Utility Theory.

## References

### 2017

- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Statistical_theory Retrieved:2017-8-17.
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**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.^{[1]}^{[2]}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.^{[2]}^{[3]}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.

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