The Annals of Statistics

Estimation of proportional covariances in the presene of certain linear restrictions

Soøren Tolver Jensen and Jesper Madsen

Full-text: Open access

Abstract

Proportionality of covariance matrices of n independent p-dimensional normal distributions with the same type of linear restrictions of the inverse covariances is considered. Conditions for existence and uniqueness of the maximum likelihood estimator are obtained through the development of general results for scale-invariant natural exponential families.

Article information

Source
Ann. Statist., Volume 32, Number 1 (2004), 219-232.

Dates
First available in Project Euclid: 12 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1079120134

Digital Object Identifier
doi:10.1214/aos/1079120134

Mathematical Reviews number (MathSciNet)
MR2051005

Zentralblatt MATH identifier
1105.62348

Subjects
Primary: 62H12: Estimation 62H15: Hypothesis testing
Secondary: 62H10: Distribution of statistics 60H20: Stochastic integral equations 62F10: Point estimation 17C50: Jordan structures associated with other structures [See also 16W10] 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]

Keywords
Proportional covariances maximum likelihood estimation profile likelihood function natural exponential families convexity Jordan algebra

Citation

Jensen, Soøren Tolver; Madsen, Jesper. Estimation of proportional covariances in the presene of certain linear restrictions. Ann. Statist. 32 (2004), no. 1, 219--232. doi:10.1214/aos/1079120134. https://projecteuclid.org/euclid.aos/1079120134


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