中文摘要：

作为绝对错误方法的一种选择，例如最不方形、最少的绝对偏差评价，一个产品亲戚错误评价为一个趋于增加的单个索引回归模型被建议。在模型的回归系数经由一个二阶段的过程被估计，他们象一致性和规度那样的统计性质被学习。包括模拟和一个身体脂肪例子的数字研究证明建议方法表现很好。

英文摘要：

As an alternative to absolute error methods, such as the least square and least absolute deviation estimations, a product relative error estimation is proposed for a multiplicative single index regression model. Regression coefficients in the model are estimated via a two-stage procedure and their statistical properties such as consistency and normality are studied. Numerical studies including simulation and a body fat example show that the proposed method performs well.