Wild bootstrap estimation in partially linear models with heteroscedasticity

This paper uses the wild bootstrap technique in the estimation of a heteroscedastic partially linear regression model. We show that this approach provides reliable approximation to the asymptotic distribution of the semiparametric least-square estimators of the linear regression coefficients and consistent estimators of the asymptotic covariance matrices even when the error variances are unequal. In comparison, this robustness property is not shared by the bootstrap estimation proposed in Liang et al. (2000. Bootstrap approximation in a partially linear regression model. J. Statist. Plann. Inference, 91, 413–426).