THE MAXIMUM LIKELIHOOD ESTIMATORS IN A MULTIVARIATE NORMAL DISTRIBUTION WITH AR(1)

COVARIANCE STRUCTURE FOR MONOTONE DATA

HIRONORI FUJISAWA

Department of Mathematics, Faculty of Science, Hiroshima University, Kagamiyama 1-3, Higashi-Hiroshima 739, Japan

(Received March 16, 1995; revised August 7, 1995)

Abstract. The maximum likelihood estimators are uniquely obtained in a multivariate normal distribution with AR(1) covariance structure for monotone data. The maximum likelihood estimator of mean is unbiased.

Key words and phrases: AR(1) covariance structure, conditional distribution, maximum likelihood estimator, missing data, monotone data, multivariate normal distribution.