## The Annals of Statistics

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

C. Villegas

#### 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

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