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Ridge regression is a popular method for dense least squares regularization. In this work, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed and a…

In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…

Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these…

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…

Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…

This paper investigates the efficient solution of penalized quadratic regressions in high-dimensional settings. A novel and efficient algorithm for ridge-penalized quadratic regression is proposed, leveraging the matrix structures of the…

Regression spline is a useful tool in nonparametric regression. However, finding the optimal knot locations is a known difficult problem. In this article, we introduce the Non-concave Penalized Regression Spline. This proposal method not…

Motivated by the CATHGEN data, we develop a new statistical learning method for simultaneous variable selection and parameter estimation under the context of generalized partly linear models for data with high-dimensional covariates. The…

We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…

In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for…

We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…

In this article, we propose a penalized high dimensional semiparametric model average quantile prediction approach that is robust for forecasting the conditional quantile of the response. We consider a two-step estimation procedure. In the…

High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…

We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…

Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse…

We investigate methods for penalized regression in the presence of missing observations. This paper introduces a method for estimating the parameters which compensates for the missing observations. We first, derive an unbiased estimator of…

For many high-dimensional studies, additional information on the variables, like (genomic) annotation or external p-values, is available. In the context of binary and continuous prediction, we develop a method for adaptive group-regularized…

The performance of penalized likelihood approaches depends profoundly on the selection of the tuning parameter; however, there is no commonly agreed-upon criterion for choosing the tuning parameter. Moreover, penalized likelihood estimation…

Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…

We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by…