中文摘要：

有单音的补品连接功能的单个索引的模型被调查。第一，连接工作，这被显示出 h (·) 能被一个图形的方法看。也就是说有水平轴上的适合的反应的阴谋；垂直的轴上的观察 y 能被用来设想连接功能。甚至当连接功能不是单音的补品时，这条图形的途径也是适用的，这被指出。注意那许多存在非参量的光滑的 ers 能也被用来估计 h (·) 。因此，经由与惩罚功能最大化协变性功能的连接功能的我花键近似在现在的工作被调查。标准的一致性被构造。小模拟被执行证实在纸建议的途径的效率。

英文摘要：

The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h（.） can be viewed by a graphic method. That is, the plot with the fitted response y on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h（.）. Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.