Extremes of the standardized Gaussian noise

Zakhar Kabluchko

Stochastic Processes and their Applications, 2011, vol. 121, issue 3, 515-533

Abstract: Let be a d-dimensional array of independent standard Gaussian random variables. For a finite set define . Let A be the number of elements in A. We prove that the appropriately normalized maximum of , where A ranges over all discrete cubes or rectangles contained in {1,...,n}d, converges in law to the Gumbel extreme-value distribution as n-->[infinity]. We also prove a continuous-time counterpart of this result.

Keywords: Extremes; Gaussian; fields; Scan; statistics; Gumbel; distribution; Pickands'; double-sum; method; Poisson; clumping; heuristics; Local; self-similarity (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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