More on least squares estimation of the transition matrix in a stationary first-order markov process from sample proportions data

Miller suggested ordinary least squares estimation of a constant transition matrix; Madansky proposed a relatively more efficient weighted least squares estimator which corrects for heteroscedasticity. In this paper an efficient generalized least squares estimator is derived which utilizes the entire covariance matrix of the distrubances. This estimator satisfies the condition that each row of the transition matrix must sum to unity. Madansky noted that estimates of the variances could be negative; a method for obtaining consistent non-negative estimates of the variances is suggested in this paper. The technique is applied to the hypothetical sample data used by Miller and Madansky.I am indebted to a referee for his thoughtful suggestions on content and style.