单指标变系数模型(SIVCM)是单指标模型和变系数模 型的推广, 具有更强的解释性. 在文章中主要利用B样条逼近技术、轮廓(profile)最小二乘方法和Levenberg-Marquardt算法研究模型指标参数和系数函数的估计问题, 证明了估计的相合性、渐近正态性, 并通过模拟研究和实例分析, 验证了提出的新方法的有效性.

The single-index variable-coefficient model, having a more effective interpretation, can be seen as a generalization of the single-index model and the variable-coefficient model. In this paper, B-spline approximation technique, profile least squares estimation and Levenberg-Marquardt algorithm are used to estimate the parameters and coefficient functions of the model, and the validity of the proposed method is verified by stochastic simulation and actual data analysis.