A Coskewness Shrinkage Approach for Estimating the Skewness of Linear Combinations of Random Variables*
提出一种协偏度矩阵的收缩估计方法，通过样本协偏度矩阵与目标矩阵的凸组合，解决小样本下估计不准的问题，并应用于对冲基金组合的均值-方差-偏度有效配置。
Abstract Decision-making in finance often requires an accurate estimate of the coskewness matrix to optimize the allocation to random variables with asymmetric distributions. The classical sample estimator of the coskewness matrix performs poorly for small sample sizes. A solution is to use shrinkage estimators, defined as the convex combination between the sample coskewness matrix and a target matrix. We propose unbiased consistent estimators for the MSE loss function and include the possibility of having multiple target matrices. In a portfolio application, we find that the proposed shrinkage coskewness estimators are useful in mean–variance–skewness efficient portfolio allocation of funds of hedge funds.