Empirical Process of Multivariate Gaussian under General Dependence

2019/10/21 by Jikai Hou, Hou, Jikai
Environmental Science · Mathematics · #Advanced Statistical Methods and Models #Analysis of environmental and stochastic processes #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1910.09319

openalex publication_date 2019/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. We give necessary and sufficient condition for the convergence in probability of the random variable sequence \sup_t\vert\widehatF_n(t)-E\widehatF_n(t)\vert\_{n∈ ℕ}, where \widehatF_n(t) is the empirical distribution. Also, we find a similar sufficient condition for almost surely convergence.

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