On Estimating the Transition Probabilities of a Markov Process

This article is concerned with estimating transition probabilities reflecting the behavior of micro units when only aggregated outcome data are available. A proposal by Miller and others relating to least squares estimates of the transition probabilities is reviewed, and alternative estimators are formulated. The estimators are applied to both actual and hypothetical data. As a result of the limited examples analyzed, it appears that the restricted least squares estimator, based on quadratic programming procedures, provides a systematic way to achieve transition probability estimates which satisfy the Goodman criterion and provides a basis for combining prior and sample information in estimating the parameters of regression and other linear statistical models.