I have a finite-state, time-independent Markov chain with two absorbing states which models educational outcomes (the absorbing states are completing and not completing). The transition probabilities are estimated by taking the proportions of people who move from one state to another at successive time points (based on a census of the population at two successive time points), and I have calculated the stationary vector.
However, since this needs to be done with several different cuts of the data, I would like to know if there is any way of associating a confidence interval to the entries of the stationary vector, to aid in identifying significant differences.
Karson, M. J. and Wrobleski, W. J. (1976),
CONFIDENCE INTERVALS FOR ABSORBING MARKOV CHAIN PROBABILITIES APPLIED TO LOAN PORTFOLIOS.
Decision Sciences, 7: 10–17.
looks helpful, but I'm not sure if it what I need. So my questions are:
Is there a way to estimate confidence intervals for the stationary vector?
and it is in the cited article, do I just need to grit my teeth and push through it, oris there a more modern treatment? (a long shot, but could save me some work) Is there is a macro or similar for SAS to estimate said confidence intervals?