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Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection
Adaptation to anisotropy inhomogeneity via dyadic piecewise polynomial selection
2011/3/23
This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous an...
Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection
anisotropy inhomogeneity piecewise polynomial
2011/3/22
This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous an...
Estimating composite functions by model selection
Curve estimation model selection composite functions
2011/3/21
We consider the problem of estimating a function $s$ on $[-1,1]^{k}$ for large values of $k$ by looking for some best approximation by composite functions of the form $g\circ u$. Our solution is based...
Consistency of Bayesian Linear Model Selection With a Growing Number of Parameters
Bayesian model selection growing number of parameters Posterior model consistency consistency of Bayes factor consistency of posterior odds ratio Gibbs sampling
2011/3/18
Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which...
The goal of cross-domain object matching (CDOM) is to find correspondence between two sets of objects in different domains in an unsupervised way. Photo album summarization is a typical application of...
Model Selection by Loss Rank for Classification and Unsupervised Learning
Classification graphical models loss rank principle model selection
2010/11/9
Hutter (2007) recently introduced the loss rank principle (LoRP) as a general-purpose principle for model selection. The LoRP enjoys many attractive prop-erties and deserves further investigations. Th...
The Loss Rank Criterion for Variable Selection in Linear Regression Analysis
Model selection lasso loss rank principle shrinkage parameter variable se-lection
2010/11/9
Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularizatio...
In linear regression problems with related predictors, it is desir-able to do variable selection and estimation by maintaining the hi-erarchical or structural relationships among predictors. In this p...
Error Prediction and Model Selection via Unbalanced Expander Graphs
Error Prediction Model Selection Unbalanced Expander Graphs
2010/10/19
We investigate deterministic design matrices for the fundamental problems of error prediction and model selection. Our deterministic design matrices are constructed from unbalanced expander graphs, a...
Stochastic model selection for Mixtures of Matrix-Normals
Mixture models birth and death process Gibbs sampler
2010/10/19
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal ...
Asymptotics and optimal bandwidth selection for highest density region estimation
Density contour density level set kernel density estimator
2010/10/14
We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HD...
High-dimensional Ising model selection using ${\ell_1}$-regularized logistic regression
High-dimensional model selection
2010/10/14
We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of...
A model selection approach to genome wide association studies
Genome wide association Multiple testing Linear regression,
2010/10/14
For the vast majority of genome wide association studies (GWAS) published so far, statistical analysis was performed by testing markers individually. In this article we present some elementary statis...
Nearly unbiased variable selection under minimax concave penalty
Variable selection model selection penalized estimation leastsquares correct selection minimax unbiasedness mean squared error
2010/3/10
We propose MC+, a fast, continuous, nearly unbiased and accu-
rate method of penalized variable selection in high-dimensional linear
regression. The LASSO is fast and continuous, but biased. The bia...
Variable selection in measurement error models
errors in variables estimating equations measurement error models non-concavepenalty function SCAD semi-parametric methods
2010/3/10
Measurement error data or errors-in-variable data have been collected in many studies. Natural
criterion functions are often unavailable for general functional measurement error models due
to the la...