On Sample Skewness and Kurtosis
推导了样本偏度和超额峰度在有限样本中的二阶偏差公式，基于AR(1)过程验证了偏差校正能有效减少偏度偏差，并在正态性检验中提升功效，但对非零偏度或峰度检验的尺寸扭曲改善有限。
It is well documented in the literature that the sample skewness and excess kurtosis can be severely biased in finite samples. In this paper, we derive analytical results for their finite-sample biases up to the second order. In general, the bias results depend on the cumulants (up to the sixth order) as well as the dependency structure of the data. Using an AR(1) process for illustration, we show that a feasible bias-correction procedure based on our analytical results works remarkably well for reducing the bias of the sample skewness. Bias-correction works reasonably well also for the sample kurtosis under some moderate degree of dependency. In terms of hypothesis testing, bias-correction offers power improvement when testing for normality, and bias-correction under the null provides also size improvement. However, for testing nonzero skewness and/or excess kurtosis, there exist nonnegligible size distortions in finite samples and bias-correction may not help.