Tail Probability of Extremes of Bivariate Isotropic Gaussian Random Fields

• Activity Number: 635
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Yuzhen Zhou*+ and Yimin Xiao
• Companies: Michigan State University and Michigan State University
• Keywords: Extremes of Random Fields ; Double sum method ; Bivariate Random Field ; Cross dependence ; Scanning statistics

Abstract

The distribution for extreme of random fields is very useful while dealing with a wide array of statistical problems, like the computation of p value in max test and the computation of the false discovery rate (abbr. FDR) in scanning statistics. Yet, most work so far only consider the real valued random field and there is few work considering tail probability of vector-valued random fields. In this paper, applying Piterbarg (1996)'s double sum method, we derive an explicit form for the probability that the supremes of bivariate Gaussian field over a set exceed a threshold simulatneously, which might extend the false discovery control problem to bivariate Gaussian random field model.