Abstract: It is of considerable interest in testing for heteroscedasticity in many practical studies. In this paper, the authors discuss this type of problem in framework of semiparametric mixed models. A global score test is proposed for the null hypothesis that all the variance components are zero. The test is based on the approaches of Lin (1997), the authors examine its performance in a simulation study, illustrate the test methods by using the progesterone data. The test can be easily implemented by using existing statistical softwares.

Key words: Heteroscedasticity, Random effects, Score test, Semiparametric regression models, Smoothing spline