## Abstract

We focus on one-sided, mixture-based stopping rules for the problem of sequential testing a simple null hypothesis against a composite alternative. For the latter, we consider two cases-either a discrete alternative or a continuous alternative that can be embedded into an exponential family. For each case, we find a mixture-based stopping rule that is nearly minimax in the sense of minimizing the maximal Kullback-Leibler information. The proof of this result is based on finding an almost Bayes rule for an appropriate sequential decision problem and on high-order asymptotic approximations for the performance characteristics of arbitrary mixture-based stopping times. We also evaluate the asymptotic performance loss of certain intuitive mixture rules and verify the accuracy of our asymptotic approximations with simulation experiments.

Original language | English (US) |
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Pages (from-to) | 297-325 |

Number of pages | 29 |

Journal | Sequential Analysis |

Volume | 31 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2012 |

Externally published | Yes |

## Keywords

- Asymptotic optimality
- Minimax tests
- Mixtures rules
- One-sided sequential tests
- Open-ended tests
- Power one tests

## ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation