Regression Diagnostics for General Linear Regression Models

For the linear regression model y = Xβ + ε the local sensitivities of estimates for β are investigated with respect to a general error structure for the residuals ε. In particular, we define local sensitivity analysis as matrix derivatives of the general least squares (GLS) estimator with respect to changes in the weight matrix ∑-1, where ∑ = var(ε). The results are extensions of derivative formulas given in Belsley, Kuh, and Welsch (1980) for ordinary least squares (OLS) regressions. An example is given showing how the new derivatives can be used for regression diagnostics in regression models with autocorrelated errors.