34,822 research outputs found
Variable selection using MM algorithms
Variable selection is fundamental to high-dimensional statistical modeling.
Many variable selection techniques may be implemented by maximum penalized
likelihood using various penalty functions. Optimizing the penalized likelihood
function is often challenging because it may be nondifferentiable and/or
nonconcave. This article proposes a new class of algorithms for finding a
maximizer of the penalized likelihood for a broad class of penalty functions.
These algorithms operate by perturbing the penalty function slightly to render
it differentiable, then optimizing this differentiable function using a
minorize-maximize (MM) algorithm. MM algorithms are useful extensions of the
well-known class of EM algorithms, a fact that allows us to analyze the local
and global convergence of the proposed algorithm using some of the techniques
employed for EM algorithms. In particular, we prove that when our MM algorithms
converge, they must converge to a desirable point; we also discuss conditions
under which this convergence may be guaranteed. We exploit the
Newton-Raphson-like aspect of these algorithms to propose a sandwich estimator
for the standard errors of the estimators. Our method performs well in
numerical tests.Comment: Published at http://dx.doi.org/10.1214/009053605000000200 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Monitoring changing geologic features along the Texas Gulf Coast
There are no author-identified significant results in this report
Charge regulation and ionic screening of patchy surfaces
The properties of surfaces with charge-regulated patches are studied using
non-linear Poisson-Boltzmann theory. Using a mode expansion to solve the
non-linear problem efficiently, we reveal the charging behaviour of
Debye-length sized patches. We find that patches charge up to higher charge
densities if their size is relatively small and if the patches are well
separated. The numerical results are used to construct a basic analytical model
which predicts the average surface charge density on surfaces with patchy
chargeable groups.Comment: 9 figure
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