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Yoshihiko Maesono 《统计学通讯:理论与方法》2013,42(2):305-327
Some statistics in common use take a form of a ratio of two statistics.In this paper, we will discuss asymptotic properties of the ratio statistic.We obtain an asymptotic representation of the ratio with remainder term o p(n -1) and a Edgeworth expansion with remainder term o(n -1/2) And as example, the asymptotic representation and the Edgeworth expansion of the jackknife skewness estimator for U-statistics are established and we discuss the biases of the skewness estimator theoretically.We also apply the result to an estimator of Pearson’s coefficient of variation and the sample correlation coefficient. 相似文献
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Yoshihiko Maesono 《统计学通讯:理论与方法》2013,42(8):1931-1942
In this paper we study the biases of jackknife estimators of central third moments which play an important role in improving the accuracy of the normal approximation. It has been found in simulation studies that the jackknife estimator of the skewness coefficient, into which the jackknife variance and third moment estimators are substituted, 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. 相似文献
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