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Zbl 1204.62144
Gapeev, Pavel V.; Küchler, Uwe
On large deviations in testing Ornstein-Uhlenbeck-type models. (English)
[J] Stat. Inference Stoch. Process. 11, No. 2, 143-155 (2008). ISSN 1387-0874; ISSN 1572-9311/e

Summary: We obtain exact large deviation rates for the log-likelihood ratio in testing models with observed Ornstein-Uhlenbeck processes and get explicit rates of decrease for the error probabilities of Neyman-Pearson, Bayes, and minimax tests. Moreover, we give expressions for the rates of decrease for the error probabilities of Neyman-Pearson tests in models with observed processes solving affine stochastic delay differential equations.

MSC 2000:: *62M02 Markov processes: hypothesis testing
60F10 Large deviations
62F05 Asymptotic properties of parametric tests
62F15 Bayesian inference
62C20 Statistical minimax procedures

Keywords: likelihood ratio; Hellinger integral; Neyman-Pearson test; Bayes test; minimax test; large deviation theorems; Girsanov formula for diffusion-type processes; Ornstein-Uhlenbeck-type process; stochastic delay differential equation

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