On the jackknife variance estimators

Research Report SRR95-003

On the jackknife variance estimators

Yoshihiko Maesono

Abstract: In this note we discuss jackknife estimators of the variance and their corrections. Shao-Wu (1989) have studied a jackknife variance estimator which is based on a delete-d original estimator. And they have proved the consistency of the delete-d jackknife variance estimator even if the original estimator is not smooth. Their results are especially useful for the jackknife estimation of the variance of the sample quantile. Whereas in the case of smooth original estimators, which include U-statistics and V-statistics, the delete-d jackknife variance estimator is numerically larger than the delete-1 jackknife estimator which is the traditional jackknife estimator. Then the delete-d jackknife variance estimator has larger bias than the delete-1.

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