Multiple hypothesis tests based On conditional differences in means

ABSTRACT

Many hypothesis tests are univariate tests and cannot cope with multiple hypothesis without an auxiliary procedure as e. g. the Bonferroni-Holm-procedure. At the same time, there is an urgent need for testing multiple hypothesis due to the very simple existing methods as the Bonferroni-correction or the Bonferroni-Holm-procedure, which suffers from a very small local significance level to detect statistical inferences or the drawback that logical and statistical dependencies among the test statistics are not used, whereby its detection is NP-hard. In honour of this occasion, we present a multiple hypothesis test for i.i.d. random variables based on conditional differences in means, which is capable to cope with multiple hypothesis and does not suffer on such drawbacks as the Bonferroni-correction or the Bonferroni-Holm-procedure. Thereby, the computation time can be neglected.

KEYWORDS:

• Conditional Differences In Means
• Multiple Hypothesis Testing
• Statistical Inferences in Multivariate Data

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H15

Notes

1 Since for independently normally distributed random variables its sum is normally distributed again, Theorem 2.1 holds in this case for every $n\in \mathbb{N}$, more precisely, $\frac{S_n-{\sum }_{i=1}^n{\mu }_i}{D_n}$ is normally distributed with mean 0 and variance 1 for for every $n\in \mathbb{N}$.

Additional information

Funding

This research work is/was funded by Bundesministerium für Landwirtschaft und Ernährung, Deichmanns Aue 29, 53168 Bonn.