Small-Sample Hypothesis Tests of Markov Order, with Application to Simulated and Hydrologic Chains
Sidney J. Yakowitz · Journal of the American Statistical Association · 1976
This paper describes admissible hypothesis tests for Markov order, the tests being defined on certain conditioned variables. In the spirit of classical hypothesis testing, the tests have the following appealing properties: The power function is constant on the hypothesis set (and, therefore, the level is not pessimistic), and the test is asymptotically most powerful within the class of tests based on regular estimators. Application of the tests herein derived to simulated and actual hydrologic data indicates that our test is superior to the usual chi-square test for Markov order, and that with moderate amounts of data, conclusions with significant physical import can be gleaned.