Confide1ce itfteefals fol transition probabilities in multi-state ma1kov cjialls
Robert E. Young, Arnold L. Sweet · Communication in Statistics- Theory and Methods · 1982
This paper is concerned with deriving approximate distributions for the maximum likelihood estimators of the transition probabilities of finite states irreduciblef aperiodic Markov chains, In a previous paper, Young and Sweet developed a procedure which becomes intractable as the number of states (s + 1) of the Markov chain becomes large, due to the fact that inversion of an (s2 +s)x(s2+ s) matrix is necessary. A decomposition method is presented which replaces the inversion of a large matrix with s(s + l)/2 inversions of matrices of size 6x6. Each inversion then yields the parameters of a marginal bivariate distribution which is similar in form to those obtained in finding the distribution for a two-state Markov chain. The two-state problem was solved in the previous papert 'and thus the desired distribution for a particular transition probability estimator is obtained. An illustrative example is given.