219,773 research outputs found
Minimax bounds for estimation of normal mixtures
This paper deals with minimax rates of convergence for estimation of density
functions on the real line. The densities are assumed to be location mixtures
of normals, a global regularity requirement that creates subtle difficulties
for the application of standard minimax lower bound methods. Using novel
Fourier and Hermite polynomial techniques, we determine the minimax optimal
rate - slightly larger than the parametric rate - under squared error loss. For
Hellinger loss, we provide a minimax lower bound using ideas modified from the
squared error loss case.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ542 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Critical curvature of large- nonlinear sigma model on
We study the nonlinear sigma model on with the gravitational
coupling term, by evaluating the effective potential in the large- limit. It
is shown that there is a critical curvature of for any positive
gravitational coupling constant , and the dynamical mass generation takes
place only when . The critical curvature is analytically found as a
function of , which leads us to define a function looking like a
natural generalization of Euler-Mascheroni constant.Comment: 7 pages, LaTe
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