Nonlinear statistical models
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Using neural networks to model conditional multivariate densities
Neural Computation
Neural modeling for time series: A statistical stepwise method for weight elimination
IEEE Transactions on Neural Networks
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This work concerns the estimation of multidimensional non-linear 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.