中文摘要：

该文讨论了带有随机设计的非参数回归模型的异方差小波检验.首先给出了回归模型的条件方差函数的经验小波系数,然后证明了它们是渐近独立和正态的.基于Fan（1996）的方法,构造了异方差检验统计量.最后通过数值模拟,作者检验了该文所提出的方法的有效性.模拟结果表明该文所提出的检验方法在水平和功效方面表现良好.

英文摘要：

The authors consider a wavelet-based test for heteroscedasticity in a nonparametric regression model with random design. The empirical wavelet coefficients of the error variance in the model are given and shown to be asympototically i.i.d, normal. Then based on the approaches of Fan.（1996）, the test statistic for heteroscedasticity is constructed. Finally, the authors examine the performance of the test in a simulation study. The test is found to perform well, in terms of both sizes and powers.