Distribution of the height of local maxima of Gaussian random fields
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| 024 | 7 | 0 | |a 10.1007/s10687-014-0211-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10687-014-0211-z | ||
| 245 | 0 | 0 | |a Distribution of the height of local maxima of Gaussian random fields |h [Elektronische Daten] |c [Dan Cheng, Armin Schwartzman] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media New York, 2014 | ||
| 690 | 7 | |a Height |2 nationallicence | |
| 690 | 7 | |a Overshoot |2 nationallicence | |
| 690 | 7 | |a Local maxima |2 nationallicence | |
| 690 | 7 | |a Riemannian manifold |2 nationallicence | |
| 690 | 7 | |a Gaussian orthogonal ensemble |2 nationallicence | |
| 690 | 7 | |a Isotropic field |2 nationallicence | |
| 690 | 7 | |a Euler characteristic |2 nationallicence | |
| 690 | 7 | |a Sphere |2 nationallicence | |
| 700 | 1 | |a Cheng |D Dan |u North Carolina State University, Raleigh, NC, USA |4 aut | |
| 700 | 1 | |a Schwartzman |D Armin |u North Carolina State University, Raleigh, NC, USA |4 aut | |
| 773 | 0 | |t Extremes |d Springer US; http://www.springer-ny.com |g 18/2(2015-06-01), 213-240 |x 1386-1999 |q 18:2<213 |1 2015 |2 18 |o 10687 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10687-014-0211-z |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10687-014-0211-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Cheng |D Dan |u North Carolina State University, Raleigh, NC, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Schwartzman |D Armin |u North Carolina State University, Raleigh, NC, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Extremes |d Springer US; http://www.springer-ny.com |g 18/2(2015-06-01), 213-240 |x 1386-1999 |q 18:2<213 |1 2015 |2 18 |o 10687 | ||