A Coskewness Shrinkage Approach for Estimating the Skewness of Linear Combinations of Random Variables

status: publishe

A coskewnesss shrinkage approach for estimating the skewness of linear combinations of random variables

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

Nearest comoment estimation with unobserved factors

We propose a minimum distance estimator for the higher-order comoments of a multivariate distribution exhibiting a lower dimensional latent factor structure. We derive the influence function of the proposed estimator and prove its consistency and asymptotic normality. The simulation study confirms the large gains in accuracy compared to the traditional sample comoments. The empirical usefulness of the novel framework is shown in applications to portfolio allocation under non-Gaussian objective functions and to the extraction of factor loadings in a dataset with mental ability scores

Robust and sparse logistic regression

Abstract: Logistic regression is one of the most popular statistical techniques for solving (binary) classification problems in various applications (e.g. credit scoring, cancer detection, ad click predictions and churn classification). Typically, the maximum likelihood estimator is used, which is very sensitive to outlying observations. In this paper, we propose a robust and sparse logistic regression estimator where robustness is achieved by means of the gamma-divergence. An elastic net penalty ensures sparsity in the regression coefficients such that the model is more stable and interpretable. We show that the influence function is bounded and demonstrate its robustness properties in simulations. The good performance of the proposed estimator is also illustrated in an empirical application that deals with classifying the type of fuel used by cars

Algorithmic portfolio tilting to harvest higher moment gains

Mean-variance-skewness-kurtosis; Non-normality; Portfolio allocation; Tilting; Statistics; Finance; Banking; Econometrics; Operations management; Business; Economics; Information science; Industr