25,064 research outputs found
Hypothesis testing near singularities and boundaries
The likelihood ratio statistic, with its asymptotic distribution at
regular model points, is often used for hypothesis testing. At model
singularities and boundaries, however, the asymptotic distribution may not be
, as highlighted by recent work of Drton. Indeed, poor behavior of a
for testing near singularities and boundaries is apparent in
simulations, and can lead to conservative or anti-conservative tests. Here we
develop a new distribution designed for use in hypothesis testing near
singularities and boundaries, which asymptotically agrees with that of the
likelihood ratio statistic. For two example trinomial models, arising in the
context of inference of evolutionary trees, we show the new distributions
outperform a .Comment: 32 pages, 12 figure
Approximating the moments of marginals of high-dimensional distributions
For probability distributions on , we study the optimal sample
size N = N(n,p) that suffices to uniformly approximate the pth moments of all
one-dimensional marginals. Under the assumption that the marginals have bounded
4p moments, we obtain the optimal bound for p > 2. This bound
goes in the direction of bridging the two recent results: a theorem of Guedon
and Rudelson [Adv. Math. 208 (2007) 798-823] which has an extra logarithmic
factor in the sample size, and a result of Adamczak et al. [J. Amer. Math. Soc.
23 (2010) 535-561] which requires stronger subexponential moment assumptions.Comment: Published in at http://dx.doi.org/10.1214/10-AOP589 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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