Locally most powerful sequential tests for discrete-time Markov processes

We consider a problem of testing H0:θ = θ0 against H1:θ > θ0, where θ is a parameter of a discrete-time Markov process. We construct a locally most powerful sequential test, which maximizes the derivative of the power function at θ = θ0 in the class of level α sequential tests with the average sample size not greater than N. We construct a locally most powerful sequential test for an AR(1) autoregressive process with an unknown location parameter as an example. © 2011 Society for Industrial and Applied Mathematics