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'''Statistika matematika''' ({{lang-en|Mathematical statistics}})
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==Introduction==
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Statistika matematika telah diilhami oleh [[:en:applied statistics|statistika terapan]] serta mengembangkan banyak prosedur pada penerapannya.
== Topik ==
Berikut adalah sejumlah topik penting dalam statistika matematika:<ref>Hogg, R. V., A. Craig, and J. W. McKean. "Intro to Mathematical Statistics." (2005).</ref><ref>Larsen, Richard J. and Marx, Morris L. "An Introduction to Mathematical Statistics and Its Applications" (2012). Prentice Hall.</ref>
=== Sebaran probabilitas ===
{{main|Sebaran probabilitas}}
[[Sebaran probabilitas]] atau "distribusi probabilitas" menggunakan [[peluang (matematika)|kemungkinan peluang atau probabilitas]] pada [[:en:measure (mathematics)|subset yang dapat diukur]] dari kemungkinan hasil suatu [[:en:Experiment (probability theory)|eksperimen]] yang bersifat acak (''random''), [[
A probability distribution can either be [[Univariate distribution|univariate]] or [[Multivariate distribution|multivariate]]. A univariate distribution gives the probabilities of a single [[random variable]] taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a [[random vector]]—a set of two or more random variables—taking on various combinations of values. Important and commonly encountered univariate probability distributions include the [[binomial distribution]], the [[hypergeometric distribution]], and the [[normal distribution]]. The [[multivariate normal distribution]] is a commonly encountered multivariate distribution.
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* a particular realization of the random process; i.e., a set of data.
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=== Regresi ===
{{main|Analisis regresi}}
Dalam [[statistika]], '''analisis regresi''' adalah suatu proses statistik untuk memperkirakan hubungan antara variabel-variabel. Termasuk di dalamnya adalah teknik-tenik untuk pembuatan model dan analisis beberapa variabel, ketika fokusnya adalah hubungan antara suatu [[:en:dependent variable|variabel dependen]] dan satu atau lebih [[:en:independent variable|variabel independen]].<!-- More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the [[conditional expectation]] of the dependent variable given the independent
Many techniques for carrying out regression analysis have been developed. Familiar methods such as [[linear regression]] and [[ordinary least squares]] regression are [[parametric statistics|parametric]], in that the regression function is defined in terms of a finite number of unknown [[parameter]]s that are estimated from the [[data]]. [[Nonparametric regression]] refers to techniques that allow the regression function to lie in a specified set of [[function (mathematics)|functions]], which may be [[dimension|infinite-dimensional]].
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=== Statistika non-parametrik ===
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Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a [[ranking]] but no clear numerical interpretation, such as when assessing [[preferences]]. In terms of [[level of measurement|levels of measurement]], non-parametric methods result in "ordinal" data.
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Another justification for the use of non-parametric methods is simplicity. In certain cases, even when the use of parametric methods is justified, non-parametric methods may be easier to use. Due both to this simplicity and to their greater robustness, non-parametric methods are seen by some statisticians as leaving less room for improper use and misunderstanding.
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==Statistika, mathematika, dan statistika matematika ==▼
Statistika matematika mempunyai ketumpangtindihan dengan bidang-bidang [[statistika]]. [[Statistikawan]] mempelajari dan memperbaiki prosedur statistika dengan matematika, dan riset statistika sering melahirkan pertanyaan matematis. Teori statistik tergantung pada [[:en:Probability theory|probabilitas]] dan [[:en:optimal decision|teori keputusan]].▼
Matematikawan dan statistikawan seperti [[Gauss]], [[Laplace]], dan [[:en:Charles Sanders Peirce|C. S. Peirce]] menggunakan [[:en:optimal decision|teori keputusan]] dengan [[sebaran probabilitas]] dan [[:en:loss function|fungsi kehilangan]] (atau [[:en:utility function|fungsi kegunaan]]). Pendekatan berdasarkan teori keputusan terhadap inferensi statistik dihidupkan kembali oleh [[:en:Abraham Wald|Abraham Wald]] dan para penerusnya,<ref>{{Cite book▼
▲Statistika matematika mempunyai ketumpangtindihan dengan bidang-bidang [[statistika]]. [[Statistikawan]] mempelajari dan memperbaiki prosedur statistika dengan matematika, dan riset statistika sering melahirkan pertanyaan matematis. Teori statistik tergantung pada [[
▲Matematikawan dan statistikawan seperti [[Gauss]], [[Laplace]], dan [[
| title = Sequential analysis▼
|last = Wald
| publisher = John Wiley and Sons▼
| location = New York▼
|url = https://archive.org/details/in.ernet.dli.2015.90255
| isbn = 0-471-91806-7▼
|year = 1947
| quote = See Dover reprint, 2004: ISBN 0-486-43912-7▼
}}</ref><ref>{{cite book
|first=Abraham
|last=Wald
|title=Statistical Decision Functions
|url=https://archive.org/details/statisticaldecis0000abra_t1e7
|year=1950
|publisher=John Wiley and Sons, New York
}}</ref><ref>{{cite book|last=Lehmann|first=Erich|authorlink=Erich Leo Lehmann
|
|isbn=0-387-94919-4 }}</ref><ref>
{{cite book
|
|
|
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▲| title=Theory of Point Estimation
▲| year=1998 |edition=2nd|isbn= 0-387-98502-6}}</ref><ref>
{{cite book
|
|
|title=Mathematical Statistics: Basic and Selected Topics
|volume=1
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|first=Lucien
|last=Le Cam
|title=Asymptotic Methods in Statistical Decision Theory
|url=https://archive.org/details/asymptoticmethod0000leca
|year=1986
|publisher=Springer-Verlag
}}</ref><ref>{{cite book
|author=Liese, Friedrich and Miescke, Klaus-J.
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|publisher=Springer
}}
</ref> serta secara ekstensif menggunakan [[
== Lihat pula ==
* {{en}} [[:en:Asymptotic theory (statistics)|Teori asimptotik]]
* [[Statistika]]
* [[Ukuran pemusatan data]]
* [[Ukuran penyebaran data]]
== Referensi ==
<references/>
== Bacaan lebih lanjut ==
* {{cite book|last= Kurnianingsih|first= Sri|authorlink=|coauthors=Kuntarti, Sulistiyono|title=Matematika SMA dan MA 2A Untuk Kelas XI Semester 1 Program IPA|year= 2007|publisher= Esis/Erlangga|location= Jakarta|id= ISBN 979-734-502-5 }} {{id icon}}
* {{cite book|last= Kurnianingsih|first= Sri|authorlink=|coauthors=Kuntarti, Sulistiyono|title=Matematika SMA dan MA 2A Untuk Kelas XI Semester 1 Program IPS|year= 2007|publisher= Esis/Erlangga|location= Jakarta|id= ISBN 979-734-563-7 }} {{id icon}}
== Pustaka tambahan ==
* Borovkov, A. A. (1999). ''Mathematical Statistics''. [[CRC Press]].
* [http://www.math.uah.edu/stat/ Virtual Laboratories in Probability and Statistics (Univ. of Ala.-Huntsville)]
* [http://www.trigonella.ch/statibot/english/ StatiBot], interactive online expert system on statistical tests.
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{{Statistika}}
{{Bidang matematika}}
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