caa a22 4500 605463956 CHVBK 20210128100255.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10687-014-0211-z doi (NATIONALLICENCE)springer-10.1007/s10687-014-0211-z Distribution of the height of local maxima of Gaussian random fields [Elektronische Daten] [Dan Cheng, Armin Schwartzman] Let {f(t) : t ∈ T} be a smooth Gaussian random field over a parameter space T, where T may be a subset of Euclidean space or, more generally, a Riemannian manifold. We provide a general formula for the distribution of the height of a local maximum ℙ{f(t 0) > u|t 0 is a local maximum of f(t)} when f is non-stationary. Moreover, we establish asymptotic approximations for the overshoot distribution of a local maximum ℙ{f(t 0) > u+v|t 0 is a local maximum of f(t) and f(t 0) > v} as v → ∞ $v\to \infty $ . Assuming further that f is isotropic, we apply techniques from random matrix theory related to the Gaussian orthogonal ensemble to compute such conditional probabilities explicitly when T is Euclidean or a sphere of arbitrary dimension. Such calculations are motivated by the statistical problem of detecting peaks in the presence of smooth Gaussian noise. Springer Science+Business Media New York, 2014 Height nationallicence Overshoot nationallicence Local maxima nationallicence Riemannian manifold nationallicence Gaussian orthogonal ensemble nationallicence Isotropic field nationallicence Euler characteristic nationallicence Sphere nationallicence Cheng Dan North Carolina State University, Raleigh, NC, USA aut Schwartzman Armin North Carolina State University, Raleigh, NC, USA aut Extremes Springer US; http://www.springer-ny.com 18/2(2015-06-01), 213-240 1386-1999 18:2<213 2015 18 10687 https://doi.org/10.1007/s10687-014-0211-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10687-014-0211-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cheng Dan North Carolina State University, Raleigh, NC, USA aut NATIONALLICENCE 700 1- Schwartzman Armin North Carolina State University, Raleigh, NC, USA aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/2(2015-06-01), 213-240 1386-1999 18:2<213 2015 18 10687