A Quadratic Programming Approach to the Estimation of Transition Probabilities

In a recent article L. G. Telser [Telser, L. G. 1963. Least-squares estimates of transition probabilities. Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld, Chapter 11, Stanford University Press, Stanford, California.] considered the problem of estimating transition probabilities in Markov processes from a set of observations on one-dimensional frequency distributions. The problem is to estimate the matrix of transition probabilities under the assumption that observations are confined to the shares of the n possibilities in successive periods. The present paper is an extension of the work of Goodman [Goodman, L. A. 1953. A further note on Miller's “finite Markov processes in psychology.” Psychometrika18 245–248.] and Telser.