Nonlinear regression modeling using regularized local likelihood method |
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Authors: | Yoshisuke Nonaka Sadanori Konishi |
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Institution: | (1) Graduate School of Mathernatics, Kyushu University, 6-10-1 Hakozaki, Higashi-Ku, 812-8581 Fukuoka, Japan;(2) Present address: Biostatistics Center, Kurume University, 67 Asahi-Machi, 830-0011 Kurume, Fukuoka, Japan |
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Abstract: | We introduce a nonlinear regression modeling strategy, using a regularized local likelihood method. The local likelihood method
is effective for analyzing data with complex structure. It might be, however, pointed out that the stability of the local
likelihood estimator is not necessarily guaranteed in the case that the structure of system is quite complex. In order to
overcome this difficulty, we propose a regularized local likelihood method with a polynomial function which unites local likelihood
and regularization. A crucial issue in constructing nonlinear regression models is the choice of a smoothing parameter, the
degree of polynomial and a regularization parameter. In order to evaluate models estimated by the regularized local likelihood
method, we derive a model selection criterion from an information-theoretic point of view. Real data analysis and Monte Carlo
experiments are conducted to examine the performance of our modeling strategy. |
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Keywords: | and phrases" target="_blank"> and phrases Information criteria local maximum likelihood estimates model selection generalized linear models regularization |
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