中文摘要：

考虑单指数模型的结构性变化检验问题，要检验连接函数是否具有线性结构．应用了小波方法来处理此问题．在给出经验小渡系数的基础上，证明了经验小波系数是渐近独立的，且具有渐近正态分布．基于此，建立了线性检验统计量．模拟结果表明，这个检验无论从水平还是功效方面都表现很好．

英文摘要：

We consider the structural test problem for single-index models. The problem is to test whether the link function is of linear structure. Wavelets are applied to cope with this problem. The empirical wavelet coefficients of the link function are given and shown to be asymptotically i. i. d. normal, based on which a test statistic for linearity of the link function is constructed. Simulation results show the test＇s good performance in terms of both sizes and powers.