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Title: Joint modelling of location, scatter matrix and skewness of multivariate skew normal distribution Authors:  Yesim Guney - Ankara University (Turkey) [presenting]
Abstract: Assuming normality of response is practical from a computational point of view and common for location and scatter matrix models, but is rather restrictive. This assumption is relaxed by using a multivariate skew-normal distribution which includes the normal distribution as a special case and provides flexibility in capturing the asymmetric behavior presented. In this case, besides the location and scatter matrix, the skewness may also be expressed with a model involving some explanatory variables along with other unknown parameters. The objective is to extend the joint mean and covariance model by considering the outcomes to follow a multivariate skew-normal distribution. We propose simultaneous modeling location, scatter matrix, and skewness models of multivariate skew normal distribution by using Pourahmadi's modified Cholesky decomposition. Specifically, our joint model handles variance heterogeneity and skewness, which are typically observed in the collection of longitudinal data from many studies. The maximum likelihood estimation method is considered for the parameters of the proposed model. In addition, numerical studies are developed to show the flexibility and versatility of the proposed model.