On the Asymptotics of Rosenblatt-Type Transformations in a Gaussian Mixture Identification Problem
On the Asymptotics of Rosenblatt-Type Transformations in a Gaussian Mixture Identification Problem
Siberian Electronic Mathematical Reports, 21, 2, pp. 1483-1502 (2024)
Abstract:
We show that a cross independence (CI) transformation of some Gaussian mixture has an asymptotically Gaussian distribution connected with the Gaussian core of the mixture by the same type of transform. We suggest using this fact for testing the fit of high-dimensional samples to a mixture of Gaussian distributions. In addition we study a behavior of extreme values in related triangular arrays.
Keywords: Gaussian mixture, multivariate copula, multivariate t distribution, extreme values, mixture identification