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.
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