The adaptive lasso is a model selection method shown to be both consistent in variable selection and asymptotically normal in coefficient estimation. The actual variable selection performance of the adaptive lasso depends on the weight used. It turns out that the weight assignment using the OLS estimate (OLS-adaptive lasso) can result in very poor performance when collinearity of the model matr...

In this paper we study post-model selection estimators which apply ordinary least squares (ols) to the model selected by first-step penalized estimators, typically lasso. It is well known that lasso can estimate the nonparametric regression function at nearly the oracle rate, and is thus hard to improve upon. We show that ols post lasso estimator performs at least as well as lasso in terms of t...

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the group Lasso in high-dimensional settings when the number of groups exceeds the sample size. We provide sufficient conditions under which the group Lasso selec...

We consider the problem of estimating a function f0 in logistic regression model. We propose to estimate this function f0 by a sparse approximation build as a linear combination of elements of a given dictionary of p functions. This sparse approximation is selected by the Lasso or Group Lasso procedure. In this context, we state non asymptotic oracle inequalities for Lasso and Group Lasso under...

When the variable of model is large, the Lasso method and the Adaptive Lasso method can effectively select variables. This paper prediction the rural residents’ consumption expenditure in China, based on respectively using the Lasso method and the Adaptive Lasso method. The results showed that both can effectively and accurately choose the appropriate variable, but the Adaptive Lasso method is ...

We consider the problem of selecting functional variables using the L1 regularization in a functional linear regression model with a scalar response and functional predictors in the presence of outliers. Since the LASSO is a special case of the penalized least squares regression with L1-penalty function it suffers from the heavy-tailed errors and/or outliers in data. Recently, the LAD regressio...

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...