English

Combining independent, arbitrarily weighted P-values: a new solution to an old problem using a novel expansion with controllable accuracy

Statistics Theory 2010-12-01 v1 Quantitative Methods Statistics Theory

Abstract

Good's formula and Fisher's method are frequently used for combining independent P-values. Interestingly, the equivalent of Good's formula already emerged in 1910 and mathematical expressions relevant to even more general situations have been repeatedly derived, albeit in different context. We provide here a novel derivation and show how the analytic formula obtained reduces to the two aforementioned ones as special cases. The main novelty of this paper, however, is the explicit treatment of nearly degenerate weights, which are known to cause numerical instabilities. We derive a controlled expansion, in powers of differences in inverse weights, that provides both accurate statistics and stable numerics.

Keywords

Cite

@article{arxiv.1011.6627,
  title  = {Combining independent, arbitrarily weighted P-values: a new solution to an old problem using a novel expansion with controllable accuracy},
  author = {Gelio Alves and Yi-Kuo Yu},
  journal= {arXiv preprint arXiv:1011.6627},
  year   = {2010}
}

Comments

16 pages, no figure

R2 v1 2026-06-21T16:51:15.297Z