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November 2014 Tail approximations for the Student $t$-, $F$-, and Welch statistics for non-normal and not necessarily i.i.d. random variables
Dmitrii Zholud
Bernoulli 20(4): 2102-2130 (November 2014). DOI: 10.3150/13-BEJ552

Abstract

Let $T$ be the Student one- or two-sample $t$-, $F$-, or Welch statistic. Now release the underlying assumptions of normality, independence and identical distribution and consider a more general case where one only assumes that the vector of data has a continuous joint density. We determine asymptotic expressions for $\mathbf{P}(T>u)$ as $u\to\infty$ for this case. The approximations are particularly accurate for small sample sizes and may be used, for example, in the analysis of High-Throughput Screening experiments, where the number of replicates can be as low as two to five and often extreme significance levels are used. We give numerous examples and complement our results by an investigation of the convergence speed – both theoretically, by deriving exact bounds for absolute and relative errors, and by means of a simulation study.

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Dmitrii Zholud. "Tail approximations for the Student $t$-, $F$-, and Welch statistics for non-normal and not necessarily i.i.d. random variables." Bernoulli 20 (4) 2102 - 2130, November 2014. https://doi.org/10.3150/13-BEJ552

Information

Published: November 2014
First available in Project Euclid: 19 September 2014

zbMATH: 1333.62053
MathSciNet: MR3263100
Digital Object Identifier: 10.3150/13-BEJ552

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 4 • November 2014
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