Email this article The use of hermite special functions for investigation of power properties of grubbs statistics
- Authors: Shiryaeva L.K1
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Affiliations:
- Samara State Economic University
- Issue: Vol 16, No 4 (2012)
- Pages: 131-145
- Section: Articles
- URL: https://ogarev-online.ru/1991-8615/article/view/20827
- ID: 20827
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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.
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##article.viewOnOriginalSite##About the authors
Ludmila K Shiryaeva
Samara State Economic University
Email: shiryeva_lk@mail.ru
(Ph. D. (Phys. & Math.)), Associate Professor, Dept. of Mathematic Statistics and Econometrics 141, Sovetskoy Armii st., Samara, 443090, Russia
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