We propose a new class of variable selection techniques for regression in high dimensional linear models based on a forward selection version of the LASSO, adaptive LASSO or elastic net, respectively to be called as forward iterative regression and shrinkage technique (FIRST), adaptive FIRST and elastic FIRST. These methods seem to work effectively for extremely sparse high dimensional linear m...

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...

We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior information into the model. In addition to quadratic programming, we employ the alternating direction method of multipliers (ADMM) and also derive an efficient solu...

This paper demonstrates the effectiveness of ensemble machine learning algorithms over the conventional multivariable linear regression models including Ordinary Least Squares, Robust Linear Model, and Lasso Model. The ensemble machine learning algorithms include Adaboost, Random-Forest, Bagging, Extremely Randomized Trees, Gradient Boosting, and Extra Trees Regressor. With the progress of open...

In this work we propose a framework for constructing goodness of fit tests in both low and high-dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or Lasso fit to the data, and using some proxy for prediction error as the final test statistic. We call this family Residual Prediction (RP) tests. We show that simul...

Variable selection is a topic of great importance in high-dimensional statistical modeling and has a wide range of real-world applications. Many variable selection techniques have been proposed in the context of linear regression, and the Lasso model is probably one of the most popular penalized regression techniques. In this paper, we propose a new, fully hierarchical, Bayesian version of the ...

One of the multiple linear regression applications in economics is Indonesia’s economic growth model based on theory endogenous growth. Endogenous development classical which cannot explain how economy grows long run. The used many independent variables, caused multicollinearity problems. In this study, using least-squares estimation method and some methods to handle problem was implemented. Va...

The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model se...