Improved residuals for linear regression models under heteroskedasticity of unknown form

Abstract

In this work we introduce a new residual for normal linear models that are suitable for situations in which we are dealing with heteroskedasticity of unknown form, they are referred to by principal component analysis (PCA) residuals. These residuals are obtained through a linear transformation of the ordinary residuals, by means of a spectral analysis on a heteroskedasticity-consistent estimator of the covariance matrix. The resulting residuals are independent and normally distributed. These residuals provide a simple way to check several assumptions that underlie the normal linear regression model, as well as model adequacy. Since they are independent and normally distributed, one may apply several results on independent random variables directly to these residuals. Finally, we provide an application to real data to illustrate the usefulness of our residuals.