Statistics and tropicalization of local field Gaussian measures

Autor:	Maazouz, Yassine El, Tran, Ngoc Mai
Rok vydání:	2019
Předmět:	Mathematics - Statistics Theory 62H05 60E05 12J25 14T90
Druh dokumentu:	Working Paper
Popis:	This paper aims to lay the foundations for statistics over local fields, such as the field of $p$-adic numbers. Over such fields, we give characterizations for maximum likelihood estimation and conditional independence for multivariate Gaussian distributions. We also give a bijection between the tropicalization of such Gaussian measures in dimension 2 and supermodular functions on the 2-dimensional discrete cube. Finally, we introduce the Bruhat-Tits building as a parameter space for Gaussian distributions and discuss their connections to conditional independence statements as an open problem. Comment: 15 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1909.00559 Zobrazit plný text záznamu View this record from Arxiv