Yuan an Lin (2004) proposed the grouped LASSO, which achieves shrinkage and selection simultaneously, as LASSO does, but works on blocks of covariates. That is, the grouped LASSO provides a model where some blocks of regression coefficients are exactly zero. The grouped LASSO is useful when there are meaningful blocks of covariates such as polynomial regression and dummy variables from categori...

The Lasso is an attractive regularisation method for high dimensional regression. It combines variable selection with an efficient computational procedure. However, the rate of convergence of the Lasso is slow for some sparse high dimensional data, where the number of predictor variables is growing fast with the number of observations. Moreover, many noise variables are selected if the estimato...

In this paper, we consider improved estimation strategies for the parameter vector in multiple regression models with first-order random coefficient autoregressive errors (RCAR(1)). We propose a shrinkage estimation strategy and implement variable selection methods such as lasso and adaptive lasso strategies. The simulation results reveal that the shrinkage estimators perform better than both l...

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...

We consider an iterated Lasso approach for variable selection and estimation in sparse, high-dimensional logistic regression models. In this approach, we use the Lasso (Tibshirani 1996) to obtain an initial estimator and reduce the dimension of the model. We then use the Lasso as the initial estimator in the adaptive Lasso (Zou 2006) to obtain the final selection and estimation results. We prov...

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...

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider `1 penalty to enforce sparsity in such scenarios. Sparsity enforcing methods, the Lasso being a canonical example, are popular candidates to address high dimension. For efficiency, they rely on tuning a parameter trading data fitting versus...

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of t...

High dimensional Poisson regression has become a standard framework for the analysis of massive counts datasets. In this work we estimate the intensity function of the Poisson regression model by using a dictionary approach, which generalizes the classical basis approach, combined with a Lasso or a group-Lasso procedure. Selection depends on penalty weights that need to be calibrated. Standard ...