%0 Journal Article
%T Penalized Spline Estimation for Nonparametric Multiplicative Regression Models
%A Wei Chen
%A Mingzhen Wan
%A Jiahui Xu
%A Jing Zhong
%A Yuying Xia
%A Minmin Zhang
%J Open Access Library Journal
%V 11
%N 4
%P 1-16
%@ 2333-9721
%D 2024
%I Open Access Library
%R 10.4236/oalib.1111352
%X In this paper, we consider the estimation problem of the unknown link function in the nonparametric multiplicative regression model. Combining the penalized splines technique, a least product relative error estimation method is proposed, where a effective model degree of freedom is defined, then the smoothing parameter is chosen by some information criterions. 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.
%K Multiplicative regression
%K Nonparametric estimation
%K Penalized splines
%K Relative error
%K Smoothing parameter selection
%U http://www.oalib.com/paper/6818576