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A skewness is a measure of symmetry of a distribution and appears in an Edgeworth expansion of a standardized or studentized statistic. It has been found in simulation studies that jackknife estimator...s of the skewness have downward biases. Fujioka and Maesono (2000) have obtained a normalizing transformation with residual term $ o(n^{-1}) $ and they pointed out that in order to construct the normalizing transformation, we need an asymptotic representation of a skewness estimator. Maesono (1998) has obtained the asymptotic representation of the jackknife skewness estimators and discussed their biases. In this paper we propose another skewness estimator of a $ U $-statistic and obtain asymptotic representations of both estimators with remainder term $ o_p(n^{-1}) $ and discuss the biases theoretically.続きを見る
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