Abstract: 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.

Key words: Regression model, Heteroscedasticity, Test, Wavelets