Geographic information systems (GIS) organize spatial data in multiple two-dimensional arrays called layers. In many applications, a response of interest is observed on a set of sites in the landscape, and it is of interest to build a regression model from the GIS layers to predict the response at unsampled sites. Model selection in this context then consists not only of selecting appropriate l...

Group lasso is a natural extension of lasso and selects variables in a grouped manner. However, group lasso suffers from estimation inefficiency and selection inconsistency. To remedy these problems, we propose the adaptive group lasso method. We show theoretically that the new method is able to identify the true model consistently, and the resulting estimator can be as efficient as oracle. Num...

The conserved threonine (Thr) residue in the penultimate position of the leader peptide of lasso peptides microcin J25 and capistruin can be effectively replaced by several amino acids close in size and shape to Thr. These findings suggest a model for lasso peptide biosynthesis in which the Thr sidechain is a recognition element for the lasso peptide maturation machinery.

The least absolute deviation (LAD) regression is a useful method for robust regression, and the least absolute shrinkage and selection operator (lasso) is a popular choice for shrinkage estimation and variable selection. In this article we combine these two classical ideas together to produce LAD-lasso. Compared with the LAD regression, LAD-lasso can do parameter estimation and variable selecti...

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted L1-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the L1-penalty. In the ul...

The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain scenarios where the lasso is inconsistent for variable selection. We then propose a new version of ...

Under the background of big data era today, once been widely used method – multiple linear regressions can not satisfy people’s need to handle big data any more because of its bad characteristics such as multicollinearity, instability, subjectivity in model chosen etc. Contrary to MLR, LASSO method has many good natures. it is stable and can handle multicollinearity and successfully select the ...

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...

Lasso is a regularization method for parameter estimation in linear models. It optimizes the model parameters with respect to a loss function subject to model complexities. This paper explores the use of lasso for statistical language modeling for text input. Owing to the very large number of parameters, directly optimizing the penalized lasso loss function is impossible. Therefore, we investig...

In this paper we use adaptive lasso estimator select between relevant and irrelevant instruments in heteroskedastic and non Gaussian data. To do so limit theory of Zou (2006) is extended from univariate iid case. Next, it is shown that adaptive lasso estimator can achieve near minimax risk bound even in the case of heteroskedastic data. To achieve that a new proof is used that benefits from Ste...