### Skapa referens, olika format (klipp och klistra)

**Harvard**

Zholud, D. (2014) *Tail approximations for the Student t-, F-, and Welch statistics for non-normal and not necessarily i.i.d. random variables*.

** BibTeX **

@article{

Zholud2014,

author={Zholud, Dmitrii},

title={Tail approximations for the Student t-, F-, and Welch statistics for non-normal and not necessarily i.i.d. random variables},

journal={Bernoulli},

issn={1350-7265},

volume={20},

issue={4},

pages={2102-2130},

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 P(T > u) as u -> infinity 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.},

year={2014},

keywords={dependent random variables, F-test, high-throughput screening, non-homogeneous data, non-normal, FALSE DISCOVERY RATES, SADDLEPOINT APPROXIMATION, MOMENT CONDITIONS},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 205364

A1 Zholud, Dmitrii

T1 Tail approximations for the Student t-, F-, and Welch statistics for non-normal and not necessarily i.i.d. random variables

YR 2014

JF Bernoulli

SN 1350-7265

VO 20

IS 4

SP 2102

OP 2130

AB 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 P(T > u) as u -> infinity 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.

LA eng

DO 10.3150/13-bej552

LK http://dx.doi.org/10.3150/13-bej552

LK http://publications.lib.chalmers.se/records/fulltext/205364/local_205364.pdf

OL 30