# Second-Order Optimal Sequential Tests

• M. B. Malyutov
• I. I. Tsitovich
Chapter
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)

## 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.

## Keywords

change-point detection controlled experiments general risk second-order optimality sequential test

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