Remarks on univariate elliptical distributions

DOI10.1016/0167-7152(90)90047-BzbMath0703.62017OpenAlexW1976317213MaRDI QIDQ916238

B. L. S. Prakasa Rao

Publication date: 1990

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(90)90047-b

zbMATH Keywords

normal distributionsquared error lossriskunbiased estimatorspherical densityelliptical densityChernoff- type inequalityestimation of linear functions of mean and standard deviationestimation of mean vectorLocally asymptotic minimax estimationlocally asymptotic minimax estimatornatural identityunivariate elliptical distribution

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Inequalities; stochastic orderings (60E15) Minimax procedures in statistical decision theory (62C20) Characterization and structure theory of statistical distributions (62E10)

Related Items (7)

Chernoff-type inequality and variance bounds ⋮ Small‐sample testing inference in symmetric and log‐symmetric linear regression models ⋮ Local power properties of some asymptotic tests in symmetric linear regression models ⋮ Unnamed Item ⋮ Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models ⋮ The order of a univariate elliptical distribution ⋮ Restricted methods in symmetrical linear regression models

Cites Work

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• On upper bounds for the variance of functions of random variables
• Robust shrinkage estimators of the location parameter for elliptically symmetric distributions
• Minimax estimation of location parameters for spherically symmetric distributions with concave loss
• Minimax estimation of location vectors for a wide class of densities
• A natural identity for exponential families with applications in multiparameter estimation
• Minimax estimation of location parameters for spherically symmetric unimodal distributions under quadratic loss
• Statistical Manifolds of Univariate Elliptic Distributions
• Characterizations of distributions through some identities

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