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 …

The usual least squares estimate of the transitional probability matrix of a finite Markov
process is given for the case in which, for each point in time, only the proportions of the …

Let X 1,⋯, XN be N observations on an m-state Markov chain with stationary transition
probability matrix P=(p_ij),p_ij>0,i,j=1,⋯,m, where N is a random variable. For any …

In this paper, situations in which individuals move through a finite set of states according to a
continuous-time Markov process are considered. Only aggregate data are available: these …

Estimation in Markov chains from aggregate data is discussed. The information about
different aspects of a chain, such as individual transition probabilities, the equilibrium …

The joint asymptotic distribution is derived for certain functions of the sample realizations of
a Markov chain with denumerably many states, from which the joint asymptotic distribution …

The paper begins with proofs of the usual theorems for the optimum properties of the
maximum-likelihood estimator of an unknown parameter θ which defines the transition …

In a recent article LG Telser [Telser, LG 1963. Least-squares estimates of transition
probabilities. Measurement in Economics: Studies in Mathematical Economics and …

In his interesting article" Finite Markov Processes in Psychology," GA Miller derived a" least-
squares estimate" for a matrix of transitional probabilities (I). However, the mathematical …

The present paper is concerned with the estimation of the transition distributions of a Markov
renewal process with finitely many states. A natural estimator of the transition distributions is …