Abstract
An asymptotic lower bound is derived involving a second additive term of order \(\sqrt {\left| {\ln \alpha } \right|} \) as α → 0 for the mean length of a controlled sequential strategy s for discrimination between two statistical models in a very general nonparametric setting. The parameter a is the maximal error probability of s.
A sequential strategy is constructed attaining (or almost attaining) this asymptotic bound uniformly over the distributions of models including those from the indifference zone. These results are extended for a general loss function g(N) with the power growth of the strategy length N.
Applications of these results to change-point detection and testing homogeneity are outlined.
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Malyutov, M.B., Tsitovich, I.I. (2001). Second-Order Optimal Sequential Tests. In: Atkinson, A., Bogacka, B., Zhigljavsky, A. (eds) Optimum Design 2000. Nonconvex Optimization and Its Applications, vol 51. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3419-5_7
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DOI: https://doi.org/10.1007/978-1-4757-3419-5_7
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