Testing a Markov hypothesis with independence of intermediate states and restricted order
Jean Thiébaux · Biometrika · 1967
SUMMARY A c-order Markov process which is independent of the intermediate states is employed as a model of protein formation; and the problem of testing a zero order hypothesis versus a general, non-zero order alternative is considered as it applies to the question of the origin of proteins. The asymptotic distributions of goodness-of-fit statistics for the transition probabilities are found for each of the collection of orders encompassed by the alternative, and the covariances of these statistics are investigated. Since the covariances are bounded away from zero, an exact test based on the maximum of the asymptotically chi-square distributed statistics was abandoned and a Monte Carlo procedure employed.