Weights of \(\overline{\chi}^2\) distribution for smooth or piecewise smooth cone alternatives

DOI10.1214/aos/1030741077zbMath0897.62055OpenAlexW1993751926MaRDI QIDQ1383084

Akimichi Takemura, Satoshi Kuriki

Publication date: 25 May 1998

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1030741077

zbMATH Keywords

second fundamental formGauss-Bonnet theoremmixed volumevolume elementShapiro's conjecturenormal meanone-sided alternativeexternal angleinternal angleone-sided simultaneous confidence regionsmooth cone alternatives

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Hypothesis testing in multivariate analysis (62H15) Mixed volumes and related topics in convex geometry (52A39)

Related Items (18)

On the equivalence of the tube and Euler characteristic methods for the distribution of the maximum of Gaussian fields over piecewise smooth domains ⋮ On testing a class of restricted hypotheses ⋮ The geometry of least squares in the 21st century ⋮ Projections on cones, chi-bar squared distributions, and Weyl's formula ⋮ Weights of \(\overline{\chi}^2\) distribution for smooth or piecewise smooth cone alternatives ⋮ A note on the power superiority of the restricted likelihood ratio test ⋮ Testing One Hypothesis Multiple Times: The Multidimensional Case ⋮ Projections on spherical cones, maximum of Gaussian fields and Rice's method. ⋮ Random fields of multivariate test statistics, with applications to shape analysis ⋮ Shrinkage estimation towards a closed convex set with a smooth boundary ⋮ Asymptotic distribution of inequality-restricted canonical correlation with application to tests for independence in ordered contingency tables ⋮ Likelihood ratio tests and singularities ⋮ Testing for Order-Restricted Hypotheses in Longitudinal Data ⋮ Analysis of multinomial models under inequality constraints: applications to measurement theory ⋮ Tail probabilities of the maxima of multilinear forms and their applications. ⋮ Variational Bayes Solution of Linear Neural Networks and Its Generalization Performance ⋮ An appraisal of some aspects of statistical inference under inequality constraints ⋮ The one-way layout with ordered parameters: a survey of advances since 1988

Cites Work

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• On Hotelling's formula for the volume of tubes and Naiman's inequality
• Testing problems with linear or angular inequality constraints
• One-sided test for the equality of two covariance matrices
• Projections on cones, chi-bar squared distributions, and Weyl's formula
• Weights of \(\overline{\chi}^2\) distribution for smooth or piecewise smooth cone alternatives
• Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints
• Non-linear angle-sum relations for polyhedral cones and polytopes
• Integrals for one-sided confidence bounds: A general result
• Testing linear hypotheses under restricted alternatives
• On the Volume of Tubes

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