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Nonlinear surface regression with dimension reduction method

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  • Takuma Yoshida

    (Kagoshima University)

Abstract

This paper considers nonlinear regression analysis with a scalar response and multiple predictors. An unknown regression function is approximated by radial basis function models. The coefficients are estimated in the context of M-estimation. It is known that ordinary M-estimation leads to overfitting in nonlinear regression. The purpose of this paper is to construct a smooth estimator. The proposed method in this paper is conducted by a two-step procedure. First, the sufficient dimension reduction methods are applied to the response and radial basis functions for transforming the large number of radial bases to a small number of linear combinations of the radial bases without loss of information. In the second step, a multiple linear regression model between a response and the transformed radial bases is assumed and the ordinary M-estimation is applied. Thus, the final estimator is also obtained as a linear combination of radial bases. The validity and an asymptotic study of the proposed method are explored. A simulation and data example are addressed to confirm the behavior of the proposed method.

Suggested Citation

  • Takuma Yoshida, 2017. "Nonlinear surface regression with dimension reduction method," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 29-50, January.
    • Handle: RePEc:spr:alstar:v:101:y:2017:i:1:d:10.1007_s10182-016-0271-2
    DOI: 10.1007/s10182-016-0271-2
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