Let X₁, X₂, …, X_n, … be a stochastic process with independent values whose distribution depends on an unknown real parameter θ. The problem of testing H₀: θ = θ₀ vs. a composite alternative H₁: θ > θ₀ is considered, where θ₀ is a fixed value of the parameter. Under some additional conditions on the distributions of the process, we present the structure of the locally most powerful (in the sense of R. Berk, Ann. Stat. 3 (1975), 373-381) sequential tests in this problem. Applications include, in particular, periodical processes, and those which are stationary starting from some fixed time point. Applications to testing hypotheses on a location parameter of autoregressive processes of finite order will be given.

Keywords: Locally most powerful; Sequential hypothesis test; Optimal stopping; One-sided composite alternative

Biography: Andrey Novikov earned his Ph. D. (Candidate of Science) degree at the Vilnius State University (Vilnius, Lithuania) in 1985. Worked as reseacher and assistant professor at the Kazan State University, Kazan, Russian Federation. Since 1998 he is a full professor at the Autonomous Metropolitan University - Iztapalapa, Mexico City, Mexico.