The least absolute shrinkage and selection operator (lasso) and ridge regression produce usually different estimates although input, loss function and parameterization of the penalty are identical. In this paper we look for ridge and lasso models with identical solution set. It turns out, that the lasso model with shrink vector λ and a quadratic penalized model with shrink matrix as outer produ...

We propose a self-tuning √ Lasso method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic) non-Gaussianity of the noise. In addition, our analysis allows for badly behaved designs, for example, perfectly collinear regressors, and generates sharp bounds even in extreme case...

MOTIVATION There has been an increasing interest in expressing a survival phenotype (e.g. time to cancer recurrence or death) or its distribution in terms of a subset of the expression data of a subset of genes. Due to high dimensionality of gene expression data, however, there is a serious problem of collinearity in fitting a prediction model, e.g. Cox's proportional hazards model. To avoid th...

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero (i.e., the solution is sparse). Moreover, statistical properties of high-dimensional lasso estimators are often proved under the assumption that the correlation between the predictors is bounded. In this vein, coordinatewise methods, the most ...

Adaptive Ridge is a special form of Ridge regression, balancing the quadratic penalization on each parameter of the model. It was shown to be equivalent to Lasso (least absolute shrinkage and selection operator), in the sense that both procedures produce the same estimate. Lasso can thus be viewed as a particular quadratic penalizer. From this observation, we derive a fixed point algorithm to c...

In this paper, a data-driven modeling technique is proposed for temperature forecasting. Due to the high dimensionality, LASSO is used as feature selection approach. Considering spatio-temporal structure of the weather dataset, first LASSO is applied in a spatial and temporal scenario, independently. Next, a feature is included in the model if it is selected by both. Finally, Least Squares Supp...

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double asymptotic framework where the maximal lag may increase with the sample size. We derive theoretical results establishing various types of consistency. In particular,...

In this paper, we use the adaptive lasso estimator to choose the relevant instruments and eliminate the irrelevant instruments. The limit theory of Zou (2006) is extended from univariate iid case to heteroskedastic and non Gaussian data. Then we use the selected instruments in generalized empirical likelihood estimators (GEL). In this sense, these are called hybrid GEL. It is also shown that th...

This paper studies the sensitivity to the observations of the block/group Lasso solution to an overdetermined linear regression model. Such a regularization is known to promote sparsity patterns structured as nonoverlapping groups of coefficients. Our main contribution provides a local parameterization of the solution with respect to the observations. As a byproduct, we give an unbiased estimat...

A Large Scale Simulation Optimization (LASSO) framework is being developed by the authors. Linux clusters are the target platform for the framework, specifically cluster resources on the NSF TeraGrid. The framework is designed in a modular fashion that simplifies coupling with simulation model executables, allowing application of simulation optimization approaches across problem domains. In thi...