We study the effective degrees of freedom of the lasso in the framework of Stein’s unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degrees of freedom of the lasso—a conclusion that requires no special assumption on the predictors. In addition, the unbiased estimator is shown to be asymptotically consistent. With these results on h...

The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the priors on the regression parameters are independent double-exponential (Laplace) distributions. This posterior can also be accessed through a Gibbs sampler using conjugate normal priors for the regression parameters, with independent exponential hyperpriors on their variances. T...

background hospitals are the most costly operational and really important units of health system because they consume about 50%-89% of total health resources. therefore efficient use of resources could help in saving and reallocating the financial and physical resources. objectives the aim of this study was to obtain an overview of hospitals' performance status by applying different techniques,...

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an attractive method for variable selection since it promotes sparsity of the groups. We study the sensitivity of any group Lasso solution to the observations and provide its precise loca...

According to the article[2], we present a new method for post-selection inference for l1(lasso)penalized likelihood models, including generalized regression models. Our approach generalizes the post-selection framework presented in Lee et al. (2013)[1]. The method provides P-values and confidence intervals that are asymptotically valid, conditional on the inherent selection done by the lasso. W...

BACKGROUND The study of circulating biomarkers and their association with disease outcomes has become progressively complex due to advances in the measurement of these biomarkers through multiplex technologies. The Least Absolute Shrinkage and Selection Operator (LASSO) is a data analysis method that may be utilized for biomarker selection in these high dimensional data. However, it is unclear ...

We congratulate the authors for an interesting article and an innovative proposal to testing the significance of the predictor variables selected by the Lasso. There is much material for thought and exploration. Research on high-dimensional regression has been very active in recent years, but most of the efforts have so far focused on estimation. Despite the popularity of the Lasso as a variabl...

The Dantzig selector (Candes and Tao, 2007) is a new approach that has been proposed for performing variable selection and model fitting on linear regression models. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso and Dantzig selector potentially do a good job of selecting the correct variables, several researcher...

In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an `-constraint on the regression coefficients has become a widely established technique. Crucial deficiencies of the lasso were unmasked when Zhou and Hastie (2005) introduced the elastic net. In this paper, we propose to extend the elastic net by admitting general nonnegative...