Matching Kollo measures
本文提出一种新方法，能同时精确匹配多元系统的均值、协方差矩阵、Kollo偏度和Kollo峰度，并给出半封闭解以提高计算效率，是首个实现四矩同时匹配的方法。
We motivate the advantages of using the Kollo measures, relative to other types of third and fourth moments of multivariate systems, and explore their Monte Carlo simulation and bootstrapping errors. Then we derive necessary and sufficient conditions for simultaneously matching any given mean vector, covariance matrix, Kollo skewness, and Kollo kurtosis. The specification of a suitable orthonormal basis greatly simplifies these moment-matching conditions. We offer semi-closed-form solutions to increase computational efficiency. In this respect, we compare our approach to two competing methods, which anyway can only match Kollo skewness and not the kurtosis at the same time. Ours is the first method for exactly matching all four multivariate moments simultaneously.