Journal of Mathematical Sciences
, Volume 139, Issue 3, pp 64976505
First online:
Student’s ttest for Gaussian scale mixtures
 N. K. BakirovAffiliated withInstitute of Mathematics
 , G. J. SzékelyAffiliated withRényi Institute of Mathematics
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A Studenttype test is constructed under a condition weaker than normal. We assume that the errors are scale mixtures of normal random variables and compute the critical values of the suggested stest. Our stest is optimal in the sense that if the level is at most α, then the stest provides the minimum critical values. (The most important critical values are tabulated at the end of the paper.) For α ≤.05, the twosided stest is identical with Student’s classical ttest. In general, the stest is a ttype test, but its degree of freedom should be reduced depending on α. The stest is applicable for many heavytailed errors, including symmetric stable, Laplace, logistic, or exponential power. Our results explain when and why the Pvalue corresponding to the tstatistic is robust if the underlying distribution is a scale mixture of normal distributions. Bibliography: 24 titles.
 Title
 Student’s ttest for Gaussian scale mixtures
 Journal

Journal of Mathematical Sciences
Volume 139, Issue 3 , pp 64976505
 Cover Date
 200612
 DOI
 10.1007/s1095800603665
 Print ISSN
 10723374
 Online ISSN
 15738795
 Publisher
 Kluwer Academic PublishersConsultants Bureau
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 Authors

 N. K. Bakirov ^{(1)}
 G. J. Székely ^{(2)}
 Author Affiliations

 1. Institute of Mathematics, Ufa, Russia
 2. Rényi Institute of Mathematics, Budapest, Hungary