Editing Mathematical statistics (section)

==Statistics, mathematics, and mathematical statistics==
Mathematical statistics is a key subset of the discipline of [[statistics]]. [[Statisticians|Statistical theorists]] study and improve statistical procedures with mathematics, and statistical research often raises mathematical questions.

Mathematicians and statisticians like [[Gauss]], [[Laplace]], and [[Charles Sanders Peirce|C. S. Peirce]] used [[optimal decision|decision theory]] with [[probability distribution]]s and [[loss function]]s (or [[utility function]]s). The decision-theoretic approach to statistical inference was reinvigorated by [[Abraham Wald]] and his successors<ref>{{Cite book
 | first = Abraham
 | last = Wald |author-link=Abraham Wald
 | title = Sequential analysis
 | year = 1947
 | publisher = John Wiley and Sons
 | location = New York
 | isbn = 0-471-91806-7
 | quote = See Dover reprint, 2004: {{isbn|0-486-43912-7}}
}}</ref><ref>{{cite book
|first=Abraham
|last=Wald
|author-link=Abraham Wald
|title=Statistical Decision Functions
|year=1950
|publisher=John Wiley and Sons, New York
}}</ref><ref>{{cite book|last=Lehmann|first=Erich|author-link=Erich Leo Lehmann
| title=Testing Statistical Hypotheses|year=1997 |edition=2nd
|isbn=0-387-94919-4 }}</ref><ref>
{{cite book 
| last1=Lehmann 
| first1=Erich
| last2=Cassella
| first2=George
| author-link1=Erich Leo Lehmann
| title=Theory of Point Estimation 
| year=1998 |edition=2nd|isbn= 0-387-98502-6}}</ref><ref>
{{cite book
| last1=Bickel|first1= Peter J.|last2=Doksum|first2=Kjell A.
| author-link1=Peter J. Bickel
|title=Mathematical Statistics: Basic and Selected Topics
|volume=1
|edition=Second (updated printing 2007) 
|year=2001
|publisher=Pearson Prentice-Hall
}}</ref><ref>{{cite book
|first=Lucien
|last=Le Cam
|author-link=Lucien Le Cam
|title=Asymptotic Methods in Statistical Decision Theory
|year=1986
|publisher=Springer-Verlag |isbn=0-387-96307-3
}}</ref><ref>{{cite book
|author1=Liese, Friedrich  |author2=Miescke, Klaus-J.
 |name-list-style=amp |title=Statistical Decision Theory: Estimation, Testing, and Selection
|year=2008
|publisher=Springer
}}
</ref> and makes extensive use of [[scientific computing]], [[mathematical analysis|analysis]], and [[Optimization (mathematics)|optimization]]; for the [[design of experiments]], statisticians use [[Algebraic statistics|algebra]] and [[Combinatorial design|combinatorics]]. But while statistical practice often relies on [[Probability theory|probability]] and [[optimal decision|decision theory]], their application can be controversial <ref name=Freedman/>