Statistical significance of rank regression

Statistical and Practical Significance of Articles at Sports Biomechanics Conferences

Background. The importance of using statistical approaches has increased and became necessary for researchers and specialists in sports biomechanics because they need more objective and accurate methods to increase knowledge. Objectives. Evaluate the reality of using practical significance in the articles published in scientific conferences in the biomechanical sport. Methods. One hundred twe...

Low rank Multivariate regression

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...

Linear Rank Regression

The errors ei in (1.1) are assumed to be independent and identically distributed, but are not necessarily normal and may be heavy-tailed. Assume for convenience that β is one dimensional. Then (1.1) is a simple linear regression. However, most of the following extends more-or-less easily to higher-dimensional β, in which case (1.1) is a multiple regression. Given β, define Ri(β) as the rank (or...

Nonparametric Reduced Rank Regression

We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a q-dimensional response, with a shared p-dimensional predictor variable. To control the complexity of the model, we employ a functional form of the Ky-Fan or nuclear norm, resulting in a set of function estimates that h...

Statistical significance and clinical significance.