Student's $t$-test for Gaussian scale mixtures
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 5-19
Voir la notice de l'article provenant de la source Math-Net.Ru
A Student type test is constructed under weaker than normal condition. We assume the errors are scale mixtures of normal random variables and compute the critical values of the suggested $s$-test. Our $s$-test is optimal in the sense that if the level is at most $\alpha$, the $s$-test provides the minimal critical values. (The most important critical values are tablulated at the end of the paper.) For $\alpha\le.05$ the two-sided $s$-test is identical with Student's classical $t$-test. In general, the $s$-test is a $t$-type test but its degree of freedom should be reduced depending on $\alpha$. The $s$-test is applicable for many heavy tailed errors including symmetric stable, Laplace, logistic, or exponential power. Our results explain when and why the $P$-value corresponding to the $t$-statistic is robust if the underlying distribution is a scale mixture of normal distributions.
@article{ZNSL_2005_328_a0,
author = {N. K. Bakirov and G. J. Szekely},
title = {Student's $t$-test for {Gaussian} scale mixtures},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {5--19},
publisher = {mathdoc},
volume = {328},
year = {2005},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a0/}
}
N. K. Bakirov; G. J. Szekely. Student's $t$-test for Gaussian scale mixtures. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 5-19. http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a0/