## The Annals of Statistics

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

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

#### 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