Penalized linear regression methods are used for the accurate prediction of new observations and to obtain interpretable models. The performance these depends on properties true coefficient vector. LASSO method is a penalized that can simultaneously perform shrinkage variable selection in continuous process. Depending structure dataset, different estimators have been proposed overcome problems ...

Background: Two main issues that challenge model building are number of Events Per Variable and multicollinearity among exploratory variables. Our aim is to review statistical methods that tackle these issues with emphasize on penalized Lasso regression model.  The present study aimed to explain problems of traditional regressions due to small sample size and m...

We consider the group lasso penalty for the linear model. We note that the standard algorithm for solving the problem assumes that the model matrices in each group are orthonormal. Here we consider a more general penalty that blends the lasso (L1) with the group lasso (“two-norm”). This penalty yields solutions that are sparse at both the group and individual feature levels. We derive an effici...

Adaptive lasso is a weighted `1 penalization method for simultaneous estimation and model selection. It has oracle properties of asymptotic normality with optimal convergence rate and model selection consistency. Instrumental variable selection has become the focus of much research in areas of application for which datasets with both strong and weak instruments are available. This paper develop...

We exhibit an approximate equivalence between the Lasso es-timator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparamet-ric regression model, as well as bounds on the p estimation loss for 1 ≤ p ≤ 2 in the linear model when the number of variables can be much larger than the sample size.

In this paper, a partially linear model based on the fused lasso method is proposed to solve problem of high correlation between adjacent variables, and then idea two-stage estimation used study solution model. Firstly, non-parametric part estimated using kernel function transforming semiparametric into parametric Secondly, regularization term introduced construct least squares parameter penalt...

Given n noisy samples with p dimensions, where n " p, we show that the multi-step thresholding procedure based on the Lasso – we call it the Thresholded Lasso, can accurately estimate a sparse vector β ∈ R in a linear model Y = Xβ + ", where Xn×p is a design matrix normalized to have column #2-norm √ n, and " ∼ N(0,σIn). We show that under the restricted eigenvalue (RE) condition (BickelRitov-T...

We define the group-lasso estimator for the natural parameters of the exponential families of distributions representing hierarchical log-linear models under multinomial sampling scheme. Such estimator arises as the solution of a convex penalized likelihood optimization problem based on the group-lasso penalty. We illustrate how it is possible to construct an estimator of the underlying log-lin...