Premium
Testing multiple hypotheses with skewed alternatives
Author(s) -
Bansal Naveen K.,
Hamedani Gholamhossein G.,
Maadooliat Mehdi
Publication year - 2016
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12430
Subject(s) - frequentist inference , false discovery rate , multiple comparisons problem , statistical hypothesis testing , computer science , bayesian probability , a priori and a posteriori , constraint (computer aided design) , prior probability , decision rule , econometrics , data mining , statistics , mathematics , bayesian inference , artificial intelligence , biochemistry , chemistry , philosophy , geometry , epistemology , gene
Summary In many practical cases of multiple hypothesis problems, it can be expected that the alternatives are not symmetrically distributed. If it is known a priori that the distributions of the alternatives are skewed, we show that this information yields high power procedures as compared to the procedures based on symmetric alternatives when testing multiple hypotheses. We propose a Bayesian decision theoretic rule for multiple directional hypothesis testing, when the alternatives are distributed as skewed, under a constraint on a mixed directional false discovery rate. We compare the proposed rule with a frequentist's rule of Benjamini and Yekutieli (2005) using simulations. We apply our method to a well‐studied HIV dataset.