39,398 research outputs found
Penalized Likelihood and Bayesian Function Selection in Regression Models
Challenging research in various fields has driven a wide range of
methodological advances in variable selection for regression models with
high-dimensional predictors. In comparison, selection of nonlinear functions in
models with additive predictors has been considered only more recently. Several
competing suggestions have been developed at about the same time and often do
not refer to each other. This article provides a state-of-the-art review on
function selection, focusing on penalized likelihood and Bayesian concepts,
relating various approaches to each other in a unified framework. In an
empirical comparison, also including boosting, we evaluate several methods
through applications to simulated and real data, thereby providing some
guidance on their performance in practice
Smoothing -penalized estimators for high-dimensional time-course data
When a series of (related) linear models has to be estimated it is often
appropriate to combine the different data-sets to construct more efficient
estimators. We use -penalized estimators like the Lasso or the Adaptive
Lasso which can simultaneously do parameter estimation and model selection. We
show that for a time-course of high-dimensional linear models the convergence
rates of the Lasso and of the Adaptive Lasso can be improved by combining the
different time-points in a suitable way. Moreover, the Adaptive Lasso still
enjoys oracle properties and consistent variable selection. The finite sample
properties of the proposed methods are illustrated on simulated data and on a
real problem of motif finding in DNA sequences.Comment: Published in at http://dx.doi.org/10.1214/07-EJS103 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Optimal designs for smoothing splines
In the common nonparametric regression model we consider the problem of constructing optimal designs, if the unknown curve is estimated by a smoothing spline. A new basis for the space of natural splines is derived, and the local minimax property for these splines is used to derive two optimality criteria for the construction of optimal designs. The first criterion determines the design for a most precise estimation of the coefficients in the spline representation and corresponds to D-optimality, while the second criterion is the G-criterion and corresponds to an accurate prediction of the curve. Several properties of the optimal designs are derived. In general D- and G-optimal designs are not equivalent. Optimal designs are determined numerically and compared with the uniform design. --smoothing spline,nonparametric regression,D- and G-optimal designs,saturated designs
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