Geodesic
The distribution of the maximum likelihood-ratio statistic used for testing a~normal sample for three outliers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 72-83

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We study the exact distribution of the likelihood-ratio statistic used for testing a normal sample for three upper (lower) outliers. We obtain recursive relationships for the integral distribution function of this statistic. We apply the obtained relationships for calculating critical values of the likelihood-ratio statistic which appear to be close to critical values of this statistic simulated by the Monte Carlo method. We give an example of the joint use of the likelihood-ratio statistic for testing a sample for more than one outlier.
Keywords: outliers, critical values, likelihood-ratio statistic, integral distribution function, testing for three upper (lower) outliers.
Mots-clés : normal distribution 
@article{IVM_2012_12_a6,
     author = {L. K. Shiryaeva},
     title = {The distribution of the maximum likelihood-ratio statistic used for testing a~normal sample for three outliers},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {72--83},
     publisher = {mathdoc},
     number = {12},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_12_a6/}
}
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L. K. Shiryaeva. The distribution of the maximum likelihood-ratio statistic used for testing a~normal sample for three outliers. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 72-83. http://geodesic.mathdoc.fr/item/IVM_2012_12_a6/