Least‐squares estimation of transition probabilities from aggregate data
John D. Kalbfleisch, Jerald F. Lawless · Canadian Journal of Statistics · 1984
Abstract Consider a population of n individuals that move independently among a finite set {1, 2,……, k} of states in a sequence of trials. t = 0. 1, 2,…, m. each according to a Markov chain with transition probability matrix P. This paper deals with the problem of estimating P on the basis of aggregate data which record only the numbers of individuals that occupy each of the k states at times t = 0. 1,2,……,m. Estimation is accomplished using conditional least squares, and asymptotic results are verified for the case n → ∞. A weighted least‐squares estimator is introduced and compared with previous estimators. Some comments are made on estimability questions that arise when only aggregate data are available.