Shrinkage estimation towards a closed convex set with a smooth boundary

zbMath0983.62033MaRDI QIDQ5926424

Akimichi Takemura, Satoshi Kuriki

Publication date: 25 April 2002

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

cone of nonnegative definite matricesgeneralized curvature measureJames-Stein estimatorsecond fundamental formWeyl's tube formula

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Geometric probability and stochastic geometry (60D05) Parametric inference under constraints (62F30)

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Cites Work

• Volumes of tubular neighborhoods of spherical polyhedra and statistical inference
• Minimax estimators that shift towards a hypersphere for location vectors of spherically symmetric distributions
• Estimation of the mean of a multivariate normal distribution
• One-sided test for the equality of two covariance matrices
• A unified approach to improving equivariant estimators
• Weights of \(\overline{\chi}^2\) distribution for smooth or piecewise smooth cone alternatives
• Some geometry of the cone of nonnegative definite matrices and weights of associated \(\overline{\chi}^2\) distribution
• The non-optimality of the inequality restricted estimator under squared error loss
• Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis
• Admissibility: Survey of a Concept in Progress
• UNBIASED ESTIMATOR OF RISK FOR AN ORTHOGONALLY INVARIANT ESTIMATOR OF A COVARIANCE MATRIX
• On the Volume of Tubes
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