Empirical Process of Multivariate Gaussian under General Dependence

10/21/2019

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by   Jikai Hou, et al.

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This paper explores certain kinds of empirical process with respect to the components of multivariate Gaussian. We put forward some finite sample bounds which hold for multivariate Gaussian under general dependence. As a direct corollary, we prove that the empirical distribution of a Gaussian process will converge, that is to say, sup_t |F_n(t) - EF_n(t) |P 0, as long as the covariance of the Gaussian process vanishes with the time shift.