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Title: Shrinkage approaches for the estimation of higher order comoments Authors:  Dries Cornilly - Vrije Universiteit Brussel (Belgium) [presenting]
Kris Boudt - Vrije Universiteit Brussel and VU Amsterdam (Belgium)
Tim Verdonck - UAntwerp, KU Leuven (Belgium)
Abstract: Optimal financial decision making often requires to take into account the higher order comoments of dependent random variables. They are however notoriously difficult to estimate. We propose several shrinkage approaches that combine the sample estimator with a structured target comoment estimate that are optimal according to a minimum distance criterion. The first contribution is in terms of the coskewness matrix where we propose unbiased estimates for the MSE loss function determining the shrinkage intensity of the multi-target shrinkage estimator. The second contribution is to obtain estimates for the higher order comoments under a latent factor model. Under this approach, we estimate the higher order comoments structurally by means of minimum distance estimation, in order to incorporate the underlying factor structure. Asymptotic normality of the estimator is proven. In both cases, the good properties are confirmed in simulations and applications on hedge fund return data.