Score tests for heteroscedasticity in wavelet regression

Abstract

We consider two score tests for heteroscedasticity in the errors of a signal-plus-noise model, where the signal is estimated by wavelet thresholding methods. The error variances are assumed to depend on observed covariates, through a parametric relationship of known form. The tests are based on the approaches of Breusch & Pagan (1979) and Koenker (1981). We establish the asymp totic validity of the tests and examine their performance in a simulation study. The Koenker test is found to perform well, in terms of both size and power.