When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that are robust against the possibility that one or several unannounced outliers may occur anywhere in the data. These methods then allow to detect outlying observa...

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...

The characterization of plant nutrients is important to understand the process of plant growth in natural ecosystems. This study attempted to evaluate the performances of univariate linear regression with various vegetation indices (VIs) and multivariate regression methods in estimating grass nutrients (i.e., nitrogen (N) and phosphorus (P)) with canopy hyperspectral reflectance. Synthetically ...

Like many other economic time series, US aggregate retail sales have strong trend and seasonal patterns. How to best model and forecast these patterns has been a long-standing issue in time-series analysis. This article compares arti"cial neural networks and traditional methods including Winters exponential smoothing, Box}Jenkins ARIMA model, and multivariate regression. The results indicate th...

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...