文章将乘积模型推广为可加乘积模型, 延伸了正测量数据的适用范围. 方法具有更强的灵活性, 同时也可避免维数祸根问题. 文中主要采用B样条逼近技术、最小乘积相对误差($LPRE$)方法, 研究非参数函数的估计问题. 并在一些条件下, 证明了非参数函数具有最优收敛速度. 最后, 通过数值模拟和实例分析, 比较了提出的方法和其它几种方法的有限样本表现, 验证了新方法的有效性.

Additive multiplicative model is a generalization of multiplicative model. It greatly extends the range of application of positive response data. Additive multiplicative model has more flexible, furthermore, it can avoid the curse of dimensionality. In this paper, we study the estimation method of additive nonparametric functions by the B-spline approximation technique and least product relative error ($LPRE$). Moreover, we prove nonparametric functions have the optimal convergence rate under some conditions. Finally, some numerical simulations and a real data analysis are given to show the finite sample performance of the proposed method.