Related papers: Post-selection inference for L1-penalized likeliho…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
This paper investigates correct variable selection in finite samples via $\ell_1$ and $\ell_1+\ell_2$ type penalization schemes. The asymptotic consistency of variable selection immediately follows from this analysis. We focus on logistic…
There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on…
We develop results for the use of Lasso and Post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, $p$. Our results apply even when $p$ is much…
In a multivariate linear regression model with $p>1$ covariates, implementation of penalization techniques often implies a preliminary univariate standardization step. Although this prevents scale effects on the covariates selection…
Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust LAD-lasso method for multiple outcomes is presented that addresses the challenges of…
In machine learning, the selection of a promising model from a potentially large number of competing models and the assessment of its generalization performance are critical tasks that need careful consideration. Typically, model selection…
We consider the framework of penalized estimation where the penalty term is given by a real-valued polyhedral gauge, which encompasses methods such as LASSO, generalized LASSO, SLOPE, OSCAR, PACS and others. Each of these estimators is…
We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to…
In applied time-to-event analysis, a flexible parametric approach is to model the hazard rate as a piecewise constant function of time. However, the change points and values of the piecewise constant hazard are usually unknown and need to…
Extracting useful information from high-dimensional data is an important focus of today's statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and…
Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing…
We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated).…
This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for…
Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods.…
The LASSO estimator is an $\ell_1$-norm penalized least-squares estimator, which was introduced for variable selection in the linear model. When the design matrix satisfies, e.g. the Restricted Isometry Property, or has a small coherence…
Simultaneous inference after model selection is of critical importance to address scientific hypotheses involving a set of parameters. In this paper, we consider high-dimensional linear regression model in which a regularization procedure…
In this paper, we propose a new method for estimation and constructing confidence intervals for low-dimensional components in a high-dimensional model. The proposed estimator, called Constrained Lasso (CLasso) estimator, is obtained by…
Variable selection methods are required in practical statistical modeling, to identify and include only the most relevant predictors, and then improving model interpretability. Such variable selection methods are typically employed in…