Consider the standard linear model y = X + ✏, where the components of ✏ are iid standard normal errors. Park and Casella [14] consider a Bayesian treatment of this model with a Laplace/Inverse-Gamma prior on ( , ). They introduce a Data Augmentation approach that can be used to explore the resulting intractable posterior density, and call it the Bayesian lasso algorithm. In this paper, the Mark...

We study the problem of variable selection for linear models under the high-dimensional asymptotic setting, where the number of observations n grows at the same rate as the number of predictors p. We consider two-stage variable selection techniques (TVS) in which the first stage uses bridge estimators to obtain an estimate of the regression coefficients, and the second stage simply thresholds t...

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is a priori known or suspected that a subset of the covariates do not significantly contribute to the overall fit of the model, a restricted model that excludes these covariates, may be sufficient. If, on the other hand, the subset provides useful information, shrinkage meth...

We consider the estimation of regression coefficients in a high-dimensional linear model. For regression coefficients in lr balls, we provide lower bounds for the minimax lq risk and minimax quantiles of the lq loss for all design matrices. Under an l0 sparsity condition on a target coefficient vector, we sharpen and unify existing oracle inequalities for the Lasso and Dantzig selector. We deri...

an analysis of the stages of crop growth presents an important step in the improvement of production management. through growth analysis, planning for planting systems, fertilization, pruning operations, harvest time as well as obtaining economical yield can be more accessible. therefore, a development of mathematical models simulating plant growth would be helpful in improving crop management,...

Purpose: preliminary discussion on model prediction precision in the partial least squares regression analysis method; Method: introduce current development conditions of partial least squares regression analysis, analyze problems of traditional regression analysis method such as multiple linear regression analysis, introduce the mathematic principle and modeling method of the partial least squ...

I use the adaptive elastic net in a Bayesian framework and test its forecasting performance against lasso, adaptive lasso and elastic net (all used in a Bayesian framework) in a series of simulations, as well as in an empirical exercise for macroeconomic Euro area data. The results suggest that elastic net is the best model among the four Bayesian methods considered. Adaptive lasso, on the othe...