On biases of jackknife estimators of third central moments

Research Report SRR95-028

On biases of jackknife estimators of third central moments

Yoshihiko Maesono

Abstract: In this paper we study biases of jackknife estimators of central third moments which take an important roll in improving the accuracy of the normal approximation. It has been found in simulation studies that the jackknife estimator of the skewness, which is substituted the jackknife variance and third moment estimators to corresponding terms, have downward biases. For the jackknife variance estimators, their asymptotic properties are precisely studied and their biases are discussed theoretically. Here we study the biases of the jackknife estimators of the central third moments for U-statistics theoretically. The results show that the biases are not always downward.

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