Estimation and Test for Multi-Dimensional Regression Models

Abstract

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour 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 paper that if we choose to minimise 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.

A Formalism of the General Mathematical Expression of Multilayer Perceptron Neural Networks

“…These models do not offer this flexibility, especially when there is at least one hidden layer and more than one output. Only their graphical form is more abundant in the literature sometimes with mathematical expression of the components [9,10]. The full expression of the functional form of three-layer MLP models with a single output is nevertheless available [11][12][13][14].…”