Turning point test: Difference between revisions
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In [[statistical hypothesis testing]], a '''turning point test''' is a statistical test of the independence of a series of random variables.<ref name="boudec">{{cite book | title = Performance Evaluation Of Computer And Communication Systems | first = Jean-Yves | last = Le Boudec | isbn = 978-2-940222-40-7 | year=2010 | publisher = EPFL Press | url = http://infoscience.epfl.ch/record/146812/files/perfPublisherVersion.pdf |pages=136-137}}</ref><ref>{{cite doi|10.1007/b97391}}</ref> |
In [[statistical hypothesis testing]], a '''turning point test''' is a statistical test of the independence of a series of random variables.<ref name="boudec">{{cite book | title = Performance Evaluation Of Computer And Communication Systems | first = Jean-Yves | last = Le Boudec | isbn = 978-2-940222-40-7 | year=2010 | publisher = EPFL Press | url = http://infoscience.epfl.ch/record/146812/files/perfPublisherVersion.pdf |pages=136-137}}</ref><ref>{{cite doi|10.1007/b97391}}</ref><ref>{{cite book | title = Time series | first= Maurice George | last = Kendall | isbn = 0852642202 | publisher = Griffin | year = 1973}}</ref> |
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==Statement of test== |
==Statement of test== |
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Revision as of 16:46, 14 June 2013
In statistical hypothesis testing, a turning point test is a statistical test of the independence of a series of random variables.[1][2][3]
Statement of test
The turning point tests the null hypothesis[1]
- H0: X1, X2, ... Xn are independent and identically distributed random variables
against
- H1: X1, X2, ... Xn are not iid.
Test statistic
We say i is a turning point if the vector X1, X2, ..., Xi, ..., Xn is not monotonic at index i.
Let T be the number of turning points then for large n, T is approximately normally distributed with mean (2n − 4)/3 and variance (16n − 29)/90. Therefore the p-value is[4]
References
- ^ a b Le Boudec, Jean-Yves (2010). Performance Evaluation Of Computer And Communication Systems (PDF). EPFL Press. pp. 136–137. ISBN 978-2-940222-40-7.
- ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/b97391, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1007/b97391instead. - ^ Kendall, Maurice George (1973). Time series. Griffin. ISBN 0852642202.
- ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/978-94-007-1861-6_4, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1007/978-94-007-1861-6_4instead.
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