Approximate Confidence Intervals for the Parameters of a Stationary Binary Markov Chain

Abstract

The power-divergence family of test statistics introduced by Cressie and Read (1984) is used to obtain approximate confidence intervals for the parameters of a stationary first-order binary Markov chain. Intervals based on inverting the likelihood ratio, Pearson, and Freeman-Tukey statistics are included in this family. Small-sample comparisons are used to select the best intervals for the different parameters. The results show that the best power-divergence intervals for the probability of success, and in particular the likelihood ratio interval, have error rates closer to nominal levels than the sample-proportion-based intervals suggested by Crow (1979). The properties of power-divergence joint-confidence regions for the transition probabilities are also explored.

KEY WORDS:

• Likelihood ratio
• Maximum likelihood
• Power-divergence family
• Transition probabilities