Multivariate normal estimation: the case (n < p)

ABSTRACT

Estimation in the multivariate context when the number of observations available is less than the number of variables is a classical theoretical problem. In order to ensure estimability, one has to assume certain constraints on the parameters. A method for maximum likelihood estimation under constraints is proposed to solve this problem. Even in the extreme case where only a single multivariate observation is available, this may provide a feasible solution. It simultaneously provides a simple, straightforward methodology to allow for specific structures within and between covariance matrices of several populations. This methodology yields exact maximum likelihood estimates.

KEYWORDS:

• Linear growth in covariance matrices
• Maximum likelihood estimation under constraints
• Observations less than parameters
• Proportional covariance matrices
• Proportional growth in covariance matrices
• Seemingly unrelated regression

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H12
• 62J02
• 62J05