Related papers: Sparse estimation via nonconcave penalized likelih…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…
Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]
Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
We propose a penalized method for the least squares estimator of a multivariate concave regression function. This estimator is formulated as a quadratic programming (QP) problem with $O(n^2)$ constraints, where n is the number of…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
Many real world practical problems can be formulated as $\ell_{0}$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative signals to underdetermined linear systems. They have been widely applied in signal…
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
The EM algorithm is a widely used methodology for penalized likelihood estimation. Provable monotonicity and convergence are the hallmarks of the EM algorithm and these properties are well established for smooth likelihood and smooth…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
This paper studies macroeconomic forecasting and variable selection using a folded-concave penalized regression with a very large number of predictors. The penalized regression approach leads to sparse estimates of the regression…
We investigate the signal reconstruction performance of sparse linear regression in the presence of noise when piecewise continuous nonconvex penalties are used. Among such penalties, we focus on the SCAD penalty. The contributions of this…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models. I-LAMM is a two-stage…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
Smoothness of the subdiagonals of the Cholesky factor of large covariance matrices is closely related to the degrees of nonstationarity of autoregressive models for time series and longitudinal data. Heuristically, one expects for a nearly…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…