Euler characteristic heuristic for approximating the distribution of the largest eigenvalue of an orthogonally invariant random matrix

DOI10.1016/j.jspi.2006.04.019zbMath1368.60057OpenAlexW2134394195MaRDI QIDQ947241

Akimichi Takemura, Satoshi Kuriki

Publication date: 29 September 2008

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2006.04.019

zbMATH Keywords

random fieldmultivariate beta distributioninverse Wishart distributionMorse's theoremtube methodwishart distribution

Mathematics Subject Classification ID

Random fields (60G60) Random fields; image analysis (62M40) Random matrices (algebraic aspects) (15B52)

Related Items (4)

The holonomic gradient method for the distribution function of the largest root of a Wishart matrix ⋮ Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix ⋮ The tube method for the moment index in projection pursuit ⋮ The volume-of-tube method for Gaussian random fields with inhomogeneous variance

Cites Work

• Euler characteristics for Gaussian fields on manifolds
• On excursion sets, tube formulas and maxima of random fields.
• Tail probabilities of the maxima of multilinear forms and their applications.
• On the equivalence of the tube and Euler characteristic methods for the distribution of the maximum of Gaussian fields over piecewise smooth domains
• Distinctness of the eigenvalues of a quadratic form in a multivariate sample
• Validity of the expected Euler characteristic heuristic
• Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ ², F and t Fields
• Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics
• Percentage points of the extreme roots of a Wishart matrix
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