Akademik Veri Yönetim Sistemi
15th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics) Working Group on Computational and Methodological Statistics (CMStatistics 2022), London, İngiltere, 17 - 19 Aralık 2022, ss.100
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.