The Annals of Statistics

Maximum Likelihood and Least Squares Estimation in Linear and Affine Functional Models

C. Villegas

Full-text: Open access

Abstract

In a linear (or affine) functional model the principal parameter is a subspace (respectively an affine subspace) in a finite dimensional inner product space, which contains the means of $n$ multivariate normal populations, all having the same covariance matrix. A relatively simple, essentially algebraic derivation of the maximum likelihood estimates is given, when these estimates are based on single observed vectors from each of the $n$ populations and an independent estimate of the common covariance matrix. A new derivation of least squares estimates is also given.

Article information

Source
Ann. Statist., Volume 10, Number 1 (1982), 256-265.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345708

Digital Object Identifier
doi:10.1214/aos/1176345708

Mathematical Reviews number (MathSciNet)
MR642737

Zentralblatt MATH identifier
0501.62020

JSTOR
links.jstor.org

Subjects
Primary: 62A05
Secondary: 62F15: Bayesian inference

Keywords
Bayesian inference logical priors inner statistical inference invariance conditional confidence multivariate analysis

Citation

Villegas, C. Maximum Likelihood and Least Squares Estimation in Linear and Affine Functional Models. Ann. Statist. 10 (1982), no. 1, 256--265. doi:10.1214/aos/1176345708. https://projecteuclid.org/euclid.aos/1176345708


Export citation