Title: Power comparison of sequential testing by betting procedures Show Chinese title

Title: 序贯检验的赌注程序比较

Abstract: In this paper, we derive power guarantees of some sequential tests for bounded mean under general alternatives. We focus on testing procedures using nonnegative supermartingales which are anytime valid and consider alternatives which coincide asymptotically with the null (e.g. vanishing mean) while still allowing to reject in finite time. Introducing variance constraints, we show that the alternative can be broaden while keeping power guarantees for certain second-order testing procedures. We also compare different test procedures in multidimensional setting using characteristics of the rejection times. Finally, we extend our analysis to other functionals as well as testing and comparing forecasters. Our results are illustrated with numerical simulations including bounded mean testing and comparison of forecasters. Show Chinese abstract

Abstract: 本文中，我们推导了在一般备择假设下一些顺序检验的功率保证。 我们关注使用非负上鞅的检验程序，这些程序随时有效，并考虑与零假设渐近一致的备择假设（例如，消失均值），同时仍然允许在有限时间内拒绝。 引入方差约束后，我们证明备择假设可以扩展，同时保持某些二阶检验程序的功率保证。 我们还使用拒绝时间的特征，在多维情况下比较不同的检验程序。 最后，我们将分析扩展到其他泛函以及检验和比较预测器。 我们的结果通过数值模拟进行了说明，包括有界均值检验和预测器比较。