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Nonlinear regression modeling via regularized radial basis function networks. (English) Zbl 1152.62039
Summary: The problem of constructing nonlinear regression models is investigated to analyze data with complex structure. We introduce radial basis functions with hyperparameters that adjusts the amount of overlapping basis functions and adopt the information of the input and response variables. By using the radial basis functions, we construct nonlinear regression models with help of the technique of regularization. Crucial issues in the model building process are the choices of a hyperparameter, the number of basis functions and a smoothing parameter.
We present information-theoretic criteria for evaluating statistical models under model misspecification both for distributional and structural assumptions. We use real data examples and Monte Carlo simulations to investigate the properties of the proposed nonlinear regression modeling techniques. The simulation results show that our nonlinear modeling performs well in various situations, and clear improvements are obtained for the use of the hyperparameter in the basis functions.

MSC:
62J02 General nonlinear regression
62B10 Statistical aspects of information-theoretic topics
65C05 Monte Carlo methods
62J12 Generalized linear models (logistic models)
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