Normal but skewed?
提出一种基于高阶对数似然导数的多元正态性检验方法，该方法渐近等价于似然比检验但只需在原假设下估计，数值上等价于所有变量线性组合的单变量偏度系数检验的上确界，蒙特卡洛模拟显示其功效优于其他方法，并应用于美国城市规模联合分布发现增长率明显非正态。
Summary We propose a multivariate normality test against skew normal distributions using higher‐order log‐likelihood derivatives, which is asymptotically equivalent to the likelihood ratio but only requires estimation under the null. Numerically, it is the supremum of the univariate skewness coefficient test over all linear combinations of the variables. We can simulate its exact finite sample distribution for any multivariate dimension and sample size. Our Monte Carlo exercises confirm its power advantages over alternative approaches. Finally, we apply it to the joint distribution of US city sizes in two consecutive censuses finding that non‐normality is very clearly seen in their growth rates.