Decision making in business and economics 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 in terms of mean squared error (MSE) when the sample size is small. A solution is to use shrinkage estimators, de ned as the convex combination between the sample coskewness matrix and a target matrix, with the aim of minimizing the MSE.
In this paper, we propose unbiased consistent estimators for the MSE loss function and include the possibility of having multiple target matrices. Simulations show that these improvements lead to a substantial reduction in the MSE when estimating the
third order comoment matrix of asymmetric distributions, as well as for the estimation of the skewness of a linear combination of random variables. In a nancial portfolio application, we nd that the proposed shrinkage coskewness estimators are e ective
in determining the linear combination with the highest expected utility.

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