  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.
