Neural networks, radial basis functions and projection pursuit regression arenonlinear models which simultaneously project the m-dimensional input data into a p-dimensional space and model nonlinear functions of the linear combinations of the inputs in this new space. Previous statistical theory for estimating the true error variance s 2 constructing approximated confidence intervals seems inappropriate, since the degrees of freedom of these models do not equal the number of adaptive parameters. We show in this article that the problem maybe overcome by using the equivalent degrees of freedom(e.d. f .) based on the dimension of the projection space. We present the results of a MonteCarlo study on simulated data showing that e.d. f . give numerical stable results and seemto work reasonably well in estimating s 2 and constructing confidence intervals
Computational studies with equivalent degrees of freedoms in neural networks
INGRASSIA, Salvatore;
2007-01-01
Abstract
Neural networks, radial basis functions and projection pursuit regression arenonlinear models which simultaneously project the m-dimensional input data into a p-dimensional space and model nonlinear functions of the linear combinations of the inputs in this new space. Previous statistical theory for estimating the true error variance s 2 constructing approximated confidence intervals seems inappropriate, since the degrees of freedom of these models do not equal the number of adaptive parameters. We show in this article that the problem maybe overcome by using the equivalent degrees of freedom(e.d. f .) based on the dimension of the projection space. We present the results of a MonteCarlo study on simulated data showing that e.d. f . give numerical stable results and seemto work reasonably well in estimating s 2 and constructing confidence intervalsFile | Dimensione | Formato | |
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