Editing Statistical theory (section)

{{Short description|Theory of statistics}}
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">
{{cite book|editor1-last=Arthanari|editor1-first=T. S.|editor2-last=Dodge|editor2-first=Yadolah|editor2-link=Yadolah Dodge|last=Rao|first=C.&nbsp;R.|author-link=C. R. Rao|chapter=Foreword| publisher=[[John Wiley & Sons]]|location=New York|year=1981|pages=vii–viii|isbn=0-471-08073-X|mr=607328| title=Mathematical Programming in Statistics}}</ref> The theory covers approaches to [[statistical decision theory|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 the  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 [[mathematical optimization|optimization]].