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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…

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $\rho=\lim\frac{p}{n}=0$, where $p$ is the dimension…

We consider a dynamical system with small noise for which the drift is parametrized by a finite dimensional parameter. For this model we consider minimum distance estimation from continuous time observations under $l^p$-penalty imposed on…

In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…

We consider penalized extremum estimation of a high-dimensional, possibly nonlinear model that is sparse in the sense that most of its parameters are zero but some are not. We use the SCAD penalty function, which provides model selection…

The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the…

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…

Using a multiplicative reparametrization, I show that a subclass of $L_q$ penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It follows that the lasso and other norm-penalized regression estimates may be obtained using a…

We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…

Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…

In this paper, we are concerned with regularized regression problems where the prior regularizer is a proper lower semicontinuous and convex function which is also partly smooth relative to a Riemannian submanifold. This encompasses as…

Generalized linear model or GLM constitutes a large class of models and essentially extends the ordinary linear regression by connecting the mean of the response variable with the covariate through appropriate link functions. On the other…

This article introduces lassopack, a suite of programs for regularized regression in Stata. lassopack implements lasso, square-root lasso, elastic net, ridge regression, adaptive lasso and post-estimation OLS. The methods are suitable for…

Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…

We introduce a new estimator for the vector of coefficients $\beta$ in the linear model $y=X\beta+z$, where $X$ has dimensions $n\times p$ with $p$ possibly larger than $n$. SLOPE, short for Sorted L-One Penalized Estimation, is the…

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the benefits of efficient loss functions.…

In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both…

We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…

This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding…