In this paper, we study the maximum likelihood estimation of the parameters of the multivariate and matrix variate symmetric Laplace distributions through group actions. The multivariate and matrix variate symmetric Laplace distributions are not in the exponential family of distributions. We relate the maximum likelihood estimation problems of these distributions to norm minimization over a group and build a correspondence between stability of data with respect to the group action and the properties of the likelihood function.

翻译：本文研究了通过群作用对多变量与矩阵变量对称拉普拉斯分布参数的最大似然估计。多变量与矩阵变量对称拉普拉斯分布不属于指数分布族。我们将这些分布的最大似然估计问题关联到群上的范数最小化，并建立了数据相对于群作用的稳定性与似然函数性质之间的对应关系。