We consider in this paper the multivariate regression problem, when the target regression matrix A is close to a low rank matrix. Our primary interest is in on the practical case where the variance of the noise is unknown. Our main contribution is to propose in this setting a criterion to select among a family of low rank estimators and prove a non-asymptotic oracle inequality for the resulting...

A “multivariate interaction” in a regression model is a product of two independent variates (linear functions of the regressors) that is an additive component of the regression function E(Y |X). In many cases a substantial portion of the overall pairwise interaction structure in a regression function can be captured by a single multivariate interaction. Due to its parsimonious form, a multivari...

We propose a new method named calibrated multivariate regression (CMR) for fitting high dimensional multivariate regression models. Compared to existing methods, CMR calibrates the regularization for each regression task with respect to its noise level so that it is simultaneously tuning insensitive and achieves an improved finite-sample performance. Computationally, we develop an efficient smo...

In many high dimensional problems, the dependence structure among the variables can be quite complex. An appropriate use of the regularization techniques coupled with other classical statistical methods can often improve estimation and prediction accuracy and facilitate model interpretation, by seeking a parsimonious model representation that involves only the subset of revelent variables. We p...

As in many areas of biostatistics, oncological problems often have multivariate predictors. While assuming a linear additive model is convenient and straightforward, it is often not satisfactory when the relation between the outcome measure and the predictors is either nonlinear or nonadditive. In addition, when the number of predictors becomes (much) larger than the number of independent obser...

In the present study, we consider the selection of model selection criteria for multivariate ridge regression. There are several model selection criteria for selecting the ridge parameter in multivariate ridge regression, e.g., the Cp criterion and the modified Cp (MCp) criterion. We propose the generalized Cp (GCp) criterion, which includes Cp andMCp criteria as special cases. The GCp criterio...