In this project, we discuss high-dimensional regression, where the dimension of the multivariate distribution is larger than the sample size, i.e. d n. With the assumption of sparse structure of the underlying multivariate distribution, we take the advantage of the `1 regularized method for parameter estimation. There are two major problems that will be discussed in this project: (1) a family o...

The Huber’s Criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. The adaptive weights in the adaptive lasso allow to have the oracle properties. In this paper we propose to combine the Huber’s criterion and adaptive penalty as lasso. This regression tech...

The purpose of the present paper is to investigate a class spherical functional autoregressive processes in order introduce and study LASSO (Least Absolute Shrinkage Selection Operator) type estimators for corresponding kernels, defined harmonic domain by means their spectral decompositions. Some crucial properties these are proved, particular, consistency oracle inequalities.

We will present an adaptation of the Least Absolute Shrinkage and Selection Operator LASSO method to the analysis of correlation dynamics of small neuronal populations. Indeed, due to its low computational cost, Lasso is an attractive regularization method for high dimensional statistical settings. Within our framework, we consider multivariate counting processes depending on an unknown functio...

The Dantzig selector (Candes and Tao, 2007) is a new approach that has been proposed for performing variable selection and model fitting on linear regression models. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso and Dantzig selector potentially do a good job of selecting the correct variables, several researcher...

BACKGROUND Multivariable confounder adjustment in comparative studies of newly marketed drugs can be limited by small numbers of exposed patients and even fewer outcomes. Disease risk scores (DRSs) developed in historical comparator drug users before the new drug entered the market may improve adjustment. However, in a high dimensional data setting, empirical selection of hundreds of potential ...

In this simple note, we attempt to further improve the sparse principal component analysis (SPCA) of Zou et al. (2006) on the following two aspects. First, we replace the traditional lasso penalty utilized in the original SPCA by the most recently developed adaptive lasso penalty (Zou, 2006; Wang et al., 2006). By doing so, adaptive amounts of shrinkage can be applied to different loading coeff...

In this paper, we forecast EU-area inflation with many predictors using time-varying parameter models. The facts that time-varying parameter models are parameter-rich and the time span of our data is relatively short motivate a desire for shrinkage. In constant coefficient regression models, the Bayesian Lasso is gaining increasing popularity as an effective tool for achieving such shrinkage. I...