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-$\psi$ tail bound is satisfied.

翻译：我们针对基于可引发与可识别泛函的一大类非参数零假设设计了序贯检验。此类泛函通过评分函数与识别函数定义，这些函数是构造零假设下非负超鞅的理想基础模块，进而通过维尔不等式导出序贯检验。利用在线凸优化的遗憾界，我们获得了针对广泛备择假设检验的渐近势的严格保证。我们的结果适用于有界与无界数据分布，仅需满足次-$\psi$尾部界假设。