Seeking relevant information from a statistical model

¹ Centro de Matemática, Universidad de la República, Iguá 4225, Malvín Norte 11400, Montevideo, Uruguay.
rfraiman@cmat.edu.uy
² Universidad de San Andrés and Conicet, Vito Dumas 284, Victoria 1644, Buenos Aires, Argentina.
yanugimenez@gmail.com; msvarc@udesa.edu.ar

Received: 19 December 2014
Revised: 13 June 2016
Accepted: 10 August 2016

Abstract

We herein introduce a general variable selection procedure, which can be applied to several parametric multivariate problems, including principal components and regression, among others. The aim is to allow the identification of a small subset of the original variables that can ‘better explain’ the model through nonparametric relationships. The method typically yields some noisy uninformative variables and some variables that are strongly related because of their general dependence and our aim is to help understand the underlying structures in a given data–set. The asymptotic behaviour of the proposed method is considered and some real and simulated data–sets are analysed as examples.