Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures
Identifieur interne : 002098 ( Main/Exploration ); précédent : 002097; suivant : 002099Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures
Auteurs : H. Finner [Allemagne] ; M. Roters [Allemagne]Source :
- Journal of Statistical Planning and Inference [ 0378-3758 ] ; 1999.
Descripteurs français
- Pascal (Inist)
- Wicri :
- topic : Méthode statistique.
English descriptors
- KwdEn :
Abstract
We consider the problem of comparing step-down and step-up multiple test procedures for testing n hypotheses when independent p-values or independent test statistics are available. The defining critical values of these procedures for independent test statistics are asymptotically equal, which yields a theoretical argument for the numerical observation that the step-up procedure is mostly more powerful than the step-down procedure. The main aim of this paper is to quantify the differences between the critical values more precisely. As a by-product we also obtain more information about the gain when we consider two subsequent steps of these procedures. Moreover, we investigate how liberal the step-up procedure becomes when the step-up critical values are replaced by their step-down counterparts or by more refined approximate values. The results for independent p-values are the basis for obtaining corresponding results when independent real-valued test statistics are at hand. It turns out that the differences of step-down and step-up critical values as well as the differences between subsequent steps tend to zero for many distributions, except for heavy-tailed distributions. The Cauchy distribution yields an example where the critical values of both procedures are nearly linearly increasing in n.
Url:
DOI: 10.1016/S0378-3758(98)00233-X
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The defining critical values of these procedures for independent test statistics are asymptotically equal, which yields a theoretical argument for the numerical observation that the step-up procedure is mostly more powerful than the step-down procedure. The main aim of this paper is to quantify the differences between the critical values more precisely. As a by-product we also obtain more information about the gain when we consider two subsequent steps of these procedures. Moreover, we investigate how liberal the step-up procedure becomes when the step-up critical values are replaced by their step-down counterparts or by more refined approximate values. The results for independent p-values are the basis for obtaining corresponding results when independent real-valued test statistics are at hand. It turns out that the differences of step-down and step-up critical values as well as the differences between subsequent steps tend to zero for many distributions, except for heavy-tailed distributions. The Cauchy distribution yields an example where the critical values of both procedures are nearly linearly increasing in n.</div></front></TEI><affiliations><list><country><li>Allemagne</li></country></list><tree><country name="Allemagne"><noRegion><name sortKey="Finner, H" sort="Finner, H" uniqKey="Finner H" first="H." last="Finner">H. Finner</name></noRegion><name sortKey="Roters, M" sort="Roters, M" uniqKey="Roters M" first="M." last="Roters">M. Roters</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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