We develop stochastic expansions with remainder o P ( 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 deﬁne a method of bandwidth choice.
Linton, Oliver B., "Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form" (1997). Cowles Foundation Discussion Papers. 1399.