2015/03/31 by Krzysztof Dȩbicki, K. Debicki, Enkelejd Hashorva +9
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #math.PR
paper · pdf · doi:10.48550/arxiv.1503.09094
21 pages
arxiv created 2015/03/31 · openalex publication_date 2015/03/31 · arxiv updated 2015/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Normal comparison lemma and Slepian's inequality are essential tools in the study of Gaussian processes. In this paper we extend normal comparison lemma and derive various related comparison inequalities including Slepian's inequality for order statistics of two Gaussian arrays.The derived results can be applied in numerous problems related to the study of the supremum of order statistics of Gaussian processes. In order to illustrate the range of possible applications, we analyze the lower tail behaviour of order statistics of self-similar Gaussian processes and derive mixed Gumbel limit theorems.