172 research outputs found
Karl Pearson's meta-analysis revisited
This paper revisits a meta-analysis method proposed by Pearson [Biometrika 26
(1934) 425--442] and first used by David [Biometrika 26 (1934) 1--11]. It was
thought to be inadmissible for over fifty years, dating back to a paper of
Birnbaum [J. Amer. Statist. Assoc. 49 (1954) 559--574]. It turns out that the
method Birnbaum analyzed is not the one that Pearson proposed. We show that
Pearson's proposal is admissible. Because it is admissible, it has better power
than the standard test of Fisher [Statistical Methods for Research Workers
(1932) Oliver and Boyd] at some alternatives, and worse power at others.
Pearson's method has the advantage when all or most of the nonzero parameters
share the same sign. Pearson's test has proved useful in a genomic setting,
screening for age-related genes. This paper also presents an FFT-based method
for getting hard upper and lower bounds on the CDF of a sum of nonnegative
random variables.Comment: Published in at http://dx.doi.org/10.1214/09-AOS697 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Local antithetic sampling with scrambled nets
We consider the problem of computing an approximation to the integral
. Monte Carlo (MC) sampling typically attains a root
mean squared error (RMSE) of from independent random function
evaluations. By contrast, quasi-Monte Carlo (QMC) sampling using carefully
equispaced evaluation points can attain the rate for
any and randomized QMC (RQMC) can attain the RMSE
, both under mild conditions on . Classical
variance reduction methods for MC can be adapted to QMC. Published results
combining QMC with importance sampling and with control variates have found
worthwhile improvements, but no change in the error rate. This paper extends
the classical variance reduction method of antithetic sampling and combines it
with RQMC. One such method is shown to bring a modest improvement in the RMSE
rate, attaining for any , for
smooth enough .Comment: Published in at http://dx.doi.org/10.1214/07-AOS548 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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