Kariya, Takeaki Equivariant estimation in a model with an ancillary statistic. (English) Zbl 0697.62020 Ann. Stat. 17, No. 2, 920-928 (1989). The author considers a model generated as an orbit under a group acting on the parameter space. A result due to R. B. Hora and R. J. Buehler [Ann. Math. Statistics 37, 643-656 (1966; Zbl 0148.138)] is generalized which concerns equivariant estimations in a model with an ancillary statistic. The established property of the estimation is used in the investigation of a model concerning the Nile problem, in a model with known variation coefficient, in a circle model and in the GMANOVA model. Reviewer: F.Liese Cited in 15 Documents MSC: 62F10 Point estimation 62A01 Foundations and philosophical topics in statistics Keywords:best equivariant estimator; sufficient statistic; curved model; MLE; normal model; maximum likelihood estimator; equivariant estimations; ancillary statistic; Nile problem; model with known variation coefficient; circle model; GMANOVA model Citations:Zbl 0148.138 × Cite Format Result Cite Review PDF Full Text: DOI