Abstract: We study the asymptotic properties of Lasso+mLS and Lasso+ Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we propose a valid inference procedure for parameter estimation based on parametric residual bootstrap after Lasso+ mLS and Lasso+Ridge. Second, we der...

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...

The least absolute shrinkage and selection operator (lasso) has been widely used in regression shrinkage and selection. In this article, we extend its application to the REGression model with AutoRegressive errors (REGAR). Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression coefficients ...

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...

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...

We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for the measurement matrices. With high probability, the developed measures for subgaussian random matrices are bounded away from zero as long as the number of me...

The restricted eigenvalue (RE) condition characterizes the sample complexity of accurate recovery in the context of high-dimensional estimators such as Lasso and Dantzig selector (Bickel et al., 2009). Recent work has shown that random design matrices drawn from any thin-tailed (subGaussian) distributions satisfy the RE condition with high probability, when the number of samples scale as the sq...

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...