Related papers: Variable selection in high-dimensional linear mode…
Doubly truncated data arise in many areas such as astronomy, econometrics, and medical studies. For the regression analysis with doubly truncated response variables, the existence of double truncation may bring bias for estimation as well…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely 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 consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects…
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…
In this paper, we consider the partially linear single-index models with longitudinal data. To deal with the variable selection problem in this context, we propose a penalized procedure combined with two bias correction methods, resulting…
Sparse group LASSO (SGL) is a penalization technique used in regression problems where the covariates have a natural grouped structure and provides solutions that are both between and within group sparse. In this paper the SGL is introduced…
We introduce GAMSEL (Generalized Additive Model Selection), a penalized likelihood approach for fitting sparse generalized additive models in high dimension. Our method interpolates between null, linear and additive models by allowing the…
In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…
Heavy-tailed error distributions and predictors with anomalous values are ubiquitous in high-dimensional regression problems and can seriously jeopardize the validity of statistical analyses if not properly addressed. For more reliable…
We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and…
In a linear instrumental variables (IV) setting for estimating the causal effects of multiple confounded exposure/treatment variables on an outcome, we investigate the adaptive Lasso method for selecting valid instrumental variables from a…
As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
In Compressed Sensing and high dimensional estimation, signal recovery often relies on sparsity assumptions and estimation is performed via $\ell_1$-penalized least-squares optimization, a.k.a. LASSO. The $\ell_1$ penalisation is usually…
Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by…
In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…
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 revisit the adaptive Lasso as well as the thresholded Lasso with refitting, in a high-dimensional linear model, and study prediction error, $\ell_q$-error ($q \in \{1, 2 \} $), and number of false positive selections. Our theoretical…