Diagnostic Tests of Distributional Shape
本文总结了在位置和尺度参数未知时，针对误差分布形状的诊断检验方法，重点介绍了近似有效得分统计量，并证明偏度和峰度分别是检验正态性对对数伽马和t分布偏离的渐近局部最优统计量。
Summary Many statistical procedures are, strictly speaking, only appropriate when a simplifying assumption about the shape of an error distribution is made, and such an assumption may need to be checked against departures in specific parametric directions. A number of ‘diagnostic’ test procedures are summarized in which location and scale may be unknown, and examples are given in the context of testing for an exponential or Gaussian shape. Approximate efficient scores are emphasized which lead to both well known and novel test statistics. In particular, we show that the standard measures of skewness and kurtosis are asymptotically locally optimal test statistics for normality against departures in the log gamma and Student t family respectively. The properties of two new test statistics are briefly investigated.