Simple BAN Estimators of Correlations for Certain Multivariate Normal Models with Known Variances

Abstract

It is well-known that in certain multivariate normal models with known variances, maximum likelihood estimation of correlations is arithmetically cumbersome. For certain of these models, a relatively simple estimation technique based on the sufficient statistics is given and shown to be best asymptotically normal. The procedure uses the fact that many of the likelihood equations for these models are essentially cubic equations. A consistent, explicit solution for the associated cubic likelihood equation is found and shown to have the appropriate efficiency and normality properties. Considered in detail are the intraclass, autoregressive, and moving average models.

Key Words:

• Maximum likelihood estimation
• Multivariate normal
• Asymptotic variance
• Intraclass model
• Autoregressive model
• Moving average model