An Exact Decomposition Theorem and a Unified View of Some Related Distributions for a Class of Exponential Transformation Models on Symmetric Cones
对称锥上指数变换模型的精确分解与相关分布的统一视角
A class of exponential transformation models is defined on symmetric cones $\Omega$ with the group of automorphisms on $\Omega$ as the acting group. We show that these models are reproductive and the exponent of their joint distribution for a given sample of size $q$ can be split into $q$ independent components, introducing one sample point at a time. The automorphism group can be factorized into the group of positive dilation and another group. Accordingly, the symmetric…