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This article is cited in 5 scientific papers (total in 5 papers)
Mathematical Modeling
Using of Special Hermite Functions for Investigation of Power Properties of Grubbs’ Criterion
L. K. Shiryaeva Samara State University of Economics, Samara, Russia
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
We consider a normal sample with a single upper outlier. A distribution of studentized form of outlier's deviation from the sample mean is obtained. This distribution uses Hermite special functions with negative integer-valued index. The integral relationships for David's power measures of Grubbs criteria are obtained. We discuss the case, when Grubbs statistic is the likelihood-ratio statistic. We find the maximal deviation of power function for Grubbs criteria from the probability that the contaminant is the outlier and it is identified as discordant. We receive the region of critical values of Grubbs statistic, where the second power measure of David equals to the third and forth power measures of David. We make calculations of power function for Grubbs criteria in the case of normal samples with a single upper outlier with the right shift. The results of calculations are similar to the theoretically expected facts.
Keywords:
outlier, Grubbs statistics, Hermite special function, David's power measures for Grubbs criterion, normal distribution law.
Original article submitted 24/VI/2012 revision submitted – 07/IX/2012
Citation:
L. K. Shiryaeva, “Using of Special Hermite Functions for Investigation of Power Properties of Grubbs’ Criterion”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(29) (2012), 131–145
Linking options:
https://www.mathnet.ru/eng/vsgtu1098 https://www.mathnet.ru/eng/vsgtu/v129/p131
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