Estimation and Test for Multi-Dimensional Regression Models

Abstract

This work is concerned with the estimation of multi-dimensional regression and the asymptotic behavior of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal estimator. We show in this article that if we choose to minimize the logarithm of the determinant of the empirical error covariance matrix, then we get an asymptotically optimal estimator. Moreover, under suitable assumptions, we show that this cost function leads to a very simple asymptotic law for testing the number of parameters of an identifiable and regular regression model. Numerical experiments confirm the theoretical results.

Keywords:

• Asymptotic normality
• Multivariate regression
• Nonlinear regression
• Test

Mathematics Subject Classification:

• Primary 62F12
• Secondary 62J02