论文标题
任何时间 - valid顺序测试可通过超级马丁的函数
Anytime-valid sequential testing for elicitable functionals via supermartingales
论文作者
论文摘要
我们设计了基于可观且可识别的功能的大型非参数零假设的顺序测试。这些功能是根据评分函数和识别函数来定义的，这是在零下构建非负超级智能的理想基础。反过来，这通过Ville的不平等进行了顺序测试。利用在线凸优化中的遗憾界限，我们可以为多种替代假设的测试的渐近能力获得严格的保证。假设满足了子$ψ$尾巴的限制，我们的结果允许有界和无限的数据分布。
We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal building blocks for constructing nonnegative supermartingales under the null. This in turn yields sequential tests via Ville's inequality. Using regret bounds from Online Convex Optimization, we obtain rigorous guarantees on the asymptotic power of the tests for a wide range of alternative hypotheses. Our results allow for bounded and unbounded data distributions, assuming that a sub-$ψ$ tail bound is satisfied.
