The tube method for the moment index in projection pursuit

DOI10.1016/j.jspi.2008.03.010zbMath1141.62054arXiv0711.3931OpenAlexW2058849286MaRDI QIDQ928909

Akimichi Takemura, Satoshi Kuriki

Publication date: 11 June 2008

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

Full work available at URL: https://arxiv.org/abs/0711.3931

zbMATH Keywords

multiple testingcritical radiusEuler characteristic heuristicsHotelling-Weyl tube formulamaxima of Gaussian random fieldssample cumulant

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Random fields (60G60) Multivariate analysis (62H99) Gaussian processes (60G15) Asymptotic distribution theory in statistics (62E20) Global differential geometry (53C99)

Related Items (3)

Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection ⋮ The volume-of-tube method for Gaussian random fields with inhomogeneous variance ⋮ Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit

Uses Software

• FastICA

Cites Work

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• Hotelling's theorem on the volume of tubes: Some illustrations in simultaneous inference and data analysis
• Euler characteristic heuristic for approximating the distribution of the largest eigenvalue of an orthogonally invariant random matrix
• Projection pursuit
• Central limit theorems for C(S)-valued random variables
• 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
• Tail probabilities of the limiting null distributions of the Anderson--Stephens statistics
• Estimating the number of peaks in a random field using the Hadwiger characteristic of excursion sets, with applications to medical images
• Tail probabilities of the maxima of Gaussian random fields
• Asymptotic distribution of inequality-restricted canonical correlation with application to tests for independence in ordered contingency tables
• Validity of the expected Euler characteristic heuristic
• Curvature Measures
• On Hotelling's Approach to Testing for a Nonlinear Parameter in Regression
• What is Projection Pursuit?
• Exploratory Projection Pursuit
• Significance levels in exploratory projection pursuit
• Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics
• Random Fields and Geometry
• Tests for randomness of directions against equatorial and bimodal alternatives
• Tubes and Spheres in n-Spaces, and a Class of Statistical Problems

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