ASYMPTOTIC REPRESENTATIONS OF SKEWNESS ESTIMATORS OF STUDENTIZED $ U $-STATISTICS
Yoshihiko Maesono · Bulletin of informatics and cybernetics · 2004
A skewness is a measure of symmetry of a distribution and appears in an Edge-worth expansion of a standardized or studentized statistic. It has been found in simulation studies that jackknife estimators of the skewness have downward bi-ases. 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 jack-knife skewness estimators and discussed their biases. In this paper we propose an-other skewness estimator of a U-statistic and obtain asymptotic representations of both estimators with remainder term op(n −1) and discuss the biases theoretically.