Nonlinear regression modeling via regularized wavelets and smoothing parameter selection

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Special Issue dedicated to Prof. FujikoshiKyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」We introduce regularized wavelet-based methods for nonlinear regression modeling when design points are not equally spaced. A crucial issue in the model building process is a choice of tuning parameters that control the smoothness of a fitted curve. We derive model selection criteria from an information-theoretic and also Bayesian approaches. Monte Carlo simulations are conducted to examine the performance of the proposed wavelet-based modeling technique.