The Huber’s Criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. The adaptive weights in the adaptive lasso allow to have the oracle properties. In this paper we propose to combine the Huber’s criterion and adaptive penalty as lasso. This regression tech...

Algorithms for simultaneous shrinkage and selection in regression and classification provide attractive solutions to knotty old statistical challenges. Nevertheless, as far as we can tell, Tibshirani’s Lasso algorithm has had little impact on statistical practice. Two particular reasons for this may be the relative inefficiency of the original Lasso algorithm and the relative complexity of more...

Penalized regression methods for simultaneous variable selection and coefficient estimation, especially those based on the lasso of Tibshirani (1996), have received a great deal of attention in recent years, mostly through frequentist models. Properties such as consistency have been studied, and are achieved by different lasso variations. Here we look at a fully Bayesian formulation of the prob...

The lasso [19] and group lasso [23] are popular algorithms in the signal processing and statistics communities. In signal processing, these algorithms allow for efficient sparse approximations of arbitrary signals in overcomplete dictionaries. In statistics, they facilitate efficient variable selection and reliable regression under the linear model assumption. In both cases, there is now ample ...

Both classical Forward Selection and the more modern Lasso provide computationally feasible methods for performing variable selection in high dimensional regression problems involving many predictors. We note that although the Lasso is the solution to an optimization problem while Forward Selection is purely algorithmic, the two methods turn out to operate in surprisingly similar fashions. Our ...

The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p > n, the lasso criterion is not strictly convex, and hence it may not have a unique minimum. An important question is: when is the lasso solution well-defined (unique)? We review results from the literature, which show that if the ...

background and objectives: constant monitoring of healthcare organizations’ performance is an integral part of informed health policy-making. several hospital performance assessment methods have been proposed in the literature. pabon lasso model offers a fast and convenient method for comparative evaluation of hospital performance. this study aimed to evaluate the relative performance of hospit...

Group LASSO is widely used to enforce the structural sparsity, which achieves the sparsity at the inter-group level. In this paper, we propose a new formulation called “exclusive group LASSO”, which brings out sparsity at intra-group level in the context of feature selection. The proposed exclusive group LASSO is applicable on any feature structures, regardless of their overlapping or non-overl...

In this paper, we discuss a parsimonious approach to estimation of high-dimensional covariance matrices via the modified Cholesky decomposition with lasso. Two different methods are proposed. They are the equiangular and equi-sparse methods. We use simulation to compare the performance of the proposed methods with others available in the literature, including the sample covariance matrix, the b...

In this paper we use adaptive lasso estimator select between relevant and irrelevant instruments in heteroskedastic and non Gaussian data. To do so limit theory of Zou (2006) is extended from univariate iid case. Next, it is shown that adaptive lasso estimator can achieve near minimax risk bound even in the case of heteroskedastic data. To achieve that a new proof is used that benefits from Ste...