Heteroscedasticity-Robustness of Jackknife Variance Estimators in Linear Models

Abstract

The asymptotic unbiasedness and consistency of three types of jackknife variance estimators in the presence of error variance heteroscedasticity in linear models are studied. The results are given in terms of the number of observations deleted and measures of imbalance of the model. The consistency of a class of Wu's weighted jackknife variance estimators for nonlinear parameters is also studied. A necessary and sufficient condition is given for the asymptotic unbiasedness and consistency of the unweighted delete-1 jackknife variance estimator and Hinkley's weighted delete-1 jackknife variance estimator. This condition is more stringent than those required for Wu's weighted jackknife. Comparison of the three delete-1 jackknife variance estimators in terms of their biases also favors the latter method.