Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures
| Autor: | M. Roters, H. Finner |
|---|---|
| Rok vydání: | 1999 |
| Předmět: |
Statistics and Probability
Basis (linear algebra) Applied Mathematics Order statistic Institut für Mathematik Cauchy distribution Critical value Distribution function Multiple comparisons problem Statistics Applied mathematics p-value Statistics Probability and Uncertainty Statistical hypothesis testing Mathematics |
| Zdroj: | Journal of Statistical Planning and Inference. 79:11-30 |
| ISSN: | 0378-3758 |
| DOI: | 10.1016/s0378-3758(98)00233-x |
| Popis: | 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 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect