COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1151

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

Oliver B. Linton

May 1997

Abstract: We develop stochastic expansions with remainder o_P(n^{–2 mu}), where 0 < mu < 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.

Keywords: Semiparametric estimation, GLS, Heteroskedasticity, Local linear regression, Asymptotic expansions