Invariantly sufficient equivariant statistics and characterizations of normality in translation classes

DOI10.1214/AOS/1176346084zbMath0533.62006OpenAlexW2084785550MaRDI QIDQ789831

Walther jun. Eberl

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1214/aos/1176346084

zbMATH Keywords

Pitman estimatorcharacterization of normalityequivariant statisticsinvariant sufficiencyminimum variance unbiased linear estimator

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Foundations and philosophical topics in statistics (62A01) Characterization and structure theory of statistical distributions (62E10) Admissibility in statistical decision theory (62C15) Sufficient statistics and fields (62B05)

Related Items (5)

A characterization of the normal distribution by sufficiency of the least squares estimation ⋮ Characterizations of normality in translation classes by properties of Bayes estimators ⋮ Simultaneous equivariant estimation of the parameters of matrix scale and matrix location-scale models ⋮ A characterization of a Gaussian process in terms of sufficient estimators ⋮ The structure of a linear model: sufficiency, ancillarity, invariance, equivariance, and the normal distribution

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