Mathematics – Statistics Theory
Scientific paper
2010-11-30
Mathematics
Statistics Theory
16 pages, no figure
Scientific paper
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.
Alves Gelio
Yu Yi-Kuo
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