Author(s)

Wei Chen^1*, Mingzhen Wan², Jiahui Xu², Jing Zhong², Yuying Xia², Minmin Zhang²

¹School of Zhangjiagang, Jiangsu University of Science and Technology, Zhangjiagang, China.
²Suzhou Institute of Technology, Jiangsu University of Science and Technology, Zhangjiagang, China.

In this paper, we consider the estimation problem of the unknown link function in the nonparametric multiplicative regression model. Combining the penalized splines technique, the least product relative error estimation method is proposed, where an effective model degree of freedom is de-fined, then the smoothing parameter is chosen by some information criteria. Simulation studies show that these strategies work well. Some asymptotic properties are established. A real data set is analyzed to illustrate the usefulness of the proposed approach. Finally, some possible extensions are discussed.

Multiplicative Regression, Nonparametric Estimation, Penalized Splines, Relative Error, Smoothing Parameter Selection

Chen, W. , Wan, M. , Xu, J. , Zhong, J. , Xia, Y. and Zhang, M. (2024) Penalized Spline Estimation for Nonparametric Multiplicative Regression Models. Open Access Library Journal, 11, 1-16. doi: 10.4236/oalib.1111352.