  This work concerns the estimation of multidimensional nonlinear regression
models using multilayer perceptrons (MLPs). The main problem with such models
is that we need to know the covariance matrix of the noise to get an optimal
estimator. However, we show in this paper that if we choose as the cost
function 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 MLP.
Numerical experiments confirm the theoretical results.
