DocumentCode :
1779669
Title :
A non-asymptotic standardization of binomial counts in Higher Criticism
Author :
Mary, D. ; Ferrari, A.
Author_Institution :
Lab. Lagrange, Univ. de Nice Sophia-Antipolis, Nice, France
fYear :
2014
fDate :
June 29 2014-July 4 2014
Firstpage :
561
Lastpage :
565
Abstract :
In the “Higher Criticism” framework for multiple hypothesis testing, the binomial counts of the empirical CDF of the P-values are standardized through Z-scores. In the asymptotic regime, the distribution of these standardized counts tends to be a standard Gaussian. In the non-asymptotic regime, these distributions depart from normality and generally differ from each other. As a result, comparable values of Z-scores obtained for different P-values reflect in fact different evidence against the joint null hypothesis. We show that such evidence can be computed in closed-form for finite sample size, resulting in an alternate standardization which leads to identically distributed and thus more comparable statistics. Numerical results illustrate some merits of the alternate standardization.
Keywords :
Gaussian processes; statistical testing; P-values; Z-scores; binomial counts; empirical CDF; finite sample size; higher criticism framework; hypothesis testing; nonasymptotic regime; nonasymptotic standardization; standard Gaussian; standardized count distribution; Approximation methods; Information theory; Joints; Random variables; Standards; Testing;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Information Theory (ISIT), 2014 IEEE International Symposium on
Conference_Location :
Honolulu, HI
Type :
conf
DOI :
10.1109/ISIT.2014.6874895
Filename :
6874895
Link To Document :
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