Delete-group Jackknife Estimate inPartially Linear Regression Models with Heteroscedasticity

Abstract Consider a partially linear regression model with anunknown vector parameter ,an unknown function g(·), andunknown heteroscedastic error variances. Chen,You^[23] proposed a semiparametricgeneralized least squares estimator (SGLSE) for, which takes theheteroscedasticity into account to increase efficiency. Forinference based on this SGLSE, it is necessary to construct aconsistent estimator for its asymptotic covariance matrix.However, when there exists within-group correlation, thetraditional delta method and the delete-1 jackknife estimationfail to offer such a consistent estimator. In this paper, bydeleting grouped partial residuals a delete-group jackknifemethod is examined. It is shown that the delete-group jackknifemethod indeed can provide a consistent estimator for theasymptotic covariance matrix in the presence of within-groupcorrelations. This result is an extension of that in[21].