Neural networks, radial basis functions and projection pursuit regression arenonlinear models which simultaneously project the m-dimensional input data into a p dimensionalspace and model nonlinear functions of the linear combinations of the inputsin this new space. Previous statistical theory for estimating the true error variance andconstructing approximated confidence intervals seems inappropriate, since the degrees offreedom of these models do not equal the number of adaptive parameters. We show inthis 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 the error variance and constructing confidence intervals
Computational experiences with equivalent degrees of freedoms / S., Ingrassia; Morlini, Isabella. - STAMPA. - 1:(2007), pp. 559-562. (Intervento presentato al convegno VI Meeting of the Classification anda Data Analysis Group of the Italian Statistical Society tenutosi a Macerata nel 12-14 Settembre 2007).
Computational experiences with equivalent degrees of freedoms
MORLINI, Isabella
2007
Abstract
Neural networks, radial basis functions and projection pursuit regression arenonlinear models which simultaneously project the m-dimensional input data into a p dimensionalspace and model nonlinear functions of the linear combinations of the inputsin this new space. Previous statistical theory for estimating the true error variance andconstructing approximated confidence intervals seems inappropriate, since the degrees offreedom of these models do not equal the number of adaptive parameters. We show inthis 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 the error variance and constructing confidence intervals
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