Nonlinear surface regression with dimension reduction method

作者：Yoshida Takuma^*

来源：ASTA-Advances in Statistical Analysis, 2017, 101(1): 29-50.

DOI：10.1007/s10182-016-0271-2

• Nonlinear surface regression
• Sliced average variance estimation
• Sliced inverse regression
• Sufficient dimension reduction

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.

• 出版日期2017-1