Star-shaped distributions and their generalizations

DOI10.1016/j.jspi.2006.03.016zbMath1145.62043arXivmath/0605600OpenAlexW2002411913MaRDI QIDQ947245

Hidehiko Kamiya, Satoshi Kuriki, Akimichi Takemura

Publication date: 29 September 2008

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

Full work available at URL: https://arxiv.org/abs/math/0605600

zbMATH Keywords

invariancenormalizerelliptically contoured distributiongroup actionequivarianceHaar measurestar-shaped setglobal cross sectionisotropy subgrouporbital decomposition

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Random matrices (algebraic aspects) (15B52)

Related Items

Polyhedral star-shaped distributions ⋮ Modelling with star-shaped distributions ⋮ Simulation of polyhedral convex contoured distributions ⋮ Geometric disintegration and star-shaped distributions ⋮ Hierarchical orbital decompositions and extended decomposable distributions ⋮ An R package for modeling and simulating generalized spherical and related distributions ⋮ High-dimensional nonparametric density estimation via symmetry and shape constraints ⋮ A unified approach to marginal equivalence in the general framework of group invariance ⋮ On \((p_{1},\dots,p_{k})\)-spherical distributions ⋮ A note on estimation of the shape of density level sets of star-shaped distributions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Distribution of eigenvalues in multivariate statistical analysis
• Some families of multivariate symmetric distributions related to exponential distribution
• Robust tests for spherical symmetry and their application to least squares regression
• Distributions of maximal invariants using quotient measures
• Inclusion-exclusion-Bonferroni identities and inequalities for discrete tube-like problems via Euler characteristics
• Robust tests for spherical symmetry
• One-sided test for the equality of two covariance matrices
• Some geometry of the cone of nonnegative definite matrices and weights of associated \(\overline{\chi}^2\) distribution
• Multivariate calculation. Use of the continuous groups
• Differential forms. With applications to the physical sciences
• Modeling and Inference with v-Spherical Distributions
• A Unified View of the Theory of Directional Statistics, 1975-1988
• Statistical analysis for the angular central Gaussian distribution on the sphere
• Some matrix-variate distribution theory: Notational considerations and a Bayesian application
• Lectures on Polytopes
• Modelling Directional Dispersion through Hyperspherical Log-Splines

This page was built for publication: Star-shaped distributions and their generalizations