Related papers: Post Selection Shrinkage Estimation for High Dimen…

Ranked set sampling (RSS) is used as a powerful data collection technique for situations where measuring the study variable requires a costly and/or tedious process while the sampling units can be ranked easily (e.g., osteoporosis…

Variable selection for structured covariates lying on an underlying known graph is a problem motivated by practical applications, and has been a topic of increasing interest. However, most of the existing methods may not be scalable to high…

Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…

We consider the problem of simultaneous variable selection and constant coefficient identification in high-dimensional varying coefficient models based on B-spline basis expansion. Both objectives can be considered as some type of model…

We consider the problem of model selection and estimation in sparse high dimensional linear regression models with strongly correlated variables. First, we study the theoretical properties of the dual Lasso solution, and we show that joint…

We introduce a new shrinkage variable selection operator for linear models which we term the \emph{adaptive ridge selector} (ARiS). This approach is inspired by the \emph{relevance vector machine} (RVM), which uses a Bayesian hierarchical…

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…

We consider the application of a popular penalised regression method, Ridge Regression, to data with very high dimensions and many more covariates than observations. Our motivation is the problem of out-of-sample prediction and the setting…

We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is…

High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…

In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…

The beta regression model is a useful framework to model response variables that are rates or proportions, that is to say, response variables which are continuous and restricted to the interval (0,1). As with any other regression model,…

One of the common challenges faced by researchers in recent data analysis is missing values. In the context of penalized linear regression, which has been extensively explored over several decades, missing values introduce bias and yield a…

In the context of multiple regression model, suppose that the vector parameter of interest \beta is subjected to lie in the subspace hypothesis H\beta = h, where this restriction is based on either additional information or prior knowledge.…

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/high-variance empirical estimate with a biased regularization estimator,…

We study the problem of high-dimensional variable selection via some two-step procedures. First we show that given some good initial estimator which is $\ell_{\infty}$-consistent but not necessarily variable selection consistent, we can…

The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and…

The uncertainty quantification and error control of classifiers are crucial in many high-consequence decision-making scenarios. We propose a selective classification framework that provides an indecision option for any observations that…