72 research outputs found
False discovery rate control with multivariate -values
Multivariate statistics are often available as well as necessary in
hypothesis tests. We study how to use such statistics to control not only false
discovery rate (FDR) but also positive FDR (pFDR) with good power. We show that
FDR can be controlled through nested regions of multivariate -values of test
statistics. If the distributions of the test statistics are known, then the
regions can be constructed explicitly to achieve FDR control with maximum power
among procedures satisfying certain conditions. On the other hand, our focus is
where the distributions are only partially known. Under certain conditions, a
type of nested regions are proposed and shown to attain (p)FDR control with
asymptotically maximum power as the pFDR control level approaches its
attainable limit. The procedure based on the nested regions is compared with
those based on other nested regions that are easier to construct as well as
those based on more straightforward combinations of the test statistics.Comment: Published in at http://dx.doi.org/10.1214/07-EJS147 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Uniform convergence of exact large deviations for renewal reward processes
Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n
just before that of X_n exceeds x>0. Motivated by stochastic models for neural
activity, uniform convergence of the form \sup_{c\in I}|a(c,x)\operatorname
{Pr}\{W(x)\gecx\}-1|=o(1), , is established for probabilities of
large deviations, with a(c,x) a deterministic function and I an open interval.
To obtain this uniform exact large deviations principle (LDP), we first
establish the exponentially fast uniform convergence of a family of renewal
measures and then apply it to appropriately tilted distributions of X_n and the
moment generating function of W(x). The uniform exact LDP is obtained for cases
where X_n has a subcomponent with a smooth density and Y_n is not a linear
transform of X_n. An extension is also made to the partial sum at the first
exceedance time.Comment: Published at http://dx.doi.org/10.1214/105051607000000023 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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