Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form

We develop stochastic expansions with remainder oP(n–2µ), where 0 < µ < 1/2, for a standardised semiparametric GLS estimator, a standard error, and a studentized statistic, in the linear regression model with heteroskedasticity of unknown form. We calculate the second moments of the truncated expansion, and use these approximations to compare two competing estimators and to de&#xfb01;ne a method of bandwidth choice.