Related papers: Penalized estimation for non-identifiable models

We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…

Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…

The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…

The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed…

The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one…

We extend the theory from Fan and Li (2001) on penalized likelihood-based estimation and model-selection to statistical and econometric models which allow for non-negativity constraints on some or all of the parameters, as well as…

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…

It has been shown in literature that the Lasso estimator, or l1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the l1-penalty allow for sharp oracle results, and then…

Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…

We consider the high-dimensional heteroscedastic regression model, where the mean and the log variance are modeled as a linear combination of input variables. Existing literature on high-dimensional linear regres- sion models has largely…

We study the asymptotic properties of the SCAD-penalized least squares estimator in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We are particularly interested in the…

Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…

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…

We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we…

Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to…

In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…

Non-concave penalized maximum likelihood methods, such as the Bridge, the SCAD, and the MCP, are widely used because they not only do parameter estimation and variable selection simultaneously but also have a high efficiency as compared to…