Penalized Spline Estimation for Nonparametric Multiplicative Regression Models

Abstract

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 defined, 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.