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Combining P-Values Via Averaging
- Source :
- SSRN Electronic Journal.
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of p-values without making any assumptions about their dependence structure. An old result by R\"uschendorf and, independently, Meng implies that the p-values can be combined by scaling up their arithmetic mean by a factor of 2 (and no smaller factor is sufficient in general). A similar result about the geometric mean (Mattner) replaces 2 by $e$. Based on more recent developments in mathematical finance, specifically, robust risk aggregation techniques, we extend these results to generalized means; in particular, we show that $K$ p-values can be combined by scaling up their harmonic mean by a factor of $\ln K$ (asymptotically as $K\to\infty$). This leads to a generalized version of the Bonferroni-Holm procedure. We also explore methods using weighted averages of p-values. Finally, we discuss the efficiency of various methods of combining p-values and how to choose a suitable method in light of data and prior information.<br />Comment: 35 pages, 3 tables, 3 figures; the main changes: correcting minor mistakes and improving the presentation
- Subjects :
- Statistics and Probability
General Mathematics
Harmonic mean
Structure (category theory)
Mathematics - Statistics Theory
Statistics Theory (math.ST)
01 natural sciences
010104 statistics & probability
0502 economics and business
FOS: Mathematics
Applied mathematics
0101 mathematics
62G10, 62F03
Scaling
Statistical hypothesis testing
Mathematics
050208 finance
Applied Mathematics
Mathematical finance
05 social sciences
Agricultural and Biological Sciences (miscellaneous)
Multiple comparisons problem
Generalized mean
Statistics, Probability and Uncertainty
Geometric mean
General Agricultural and Biological Sciences
Weighted arithmetic mean
Arithmetic mean
Subjects
Details
- ISSN :
- 15565068
- Database :
- OpenAIRE
- Journal :
- SSRN Electronic Journal
- Accession number :
- edsair.doi.dedup.....c66ff834b66cc2fff5d0d990bf4a5db1