Estimation of Finite Population Transition Probability Matrix Based on Two Stage Sampling Design

Abstract

We consider the problem of estimation of the transition probabilities of a Markov chain from survey data based on a complex sampling design. A finite population estimation procedure for estimating the transition probabilities of a finite state time-homogeneous bivariate Markov chain, that may be used to model an intergenerational social mobility problem, is presented. The estimators based on two stage sampling design when both the first stage and second stage samples are selected according to simple random sampling without replacement are proposed. We provide the bias and mean square error of the proposed estimators. Further, based on empirical data we also calculate the estimated biases and estimated mean square errors.