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math.ST2025
A Generalisation of Ville's Inequality to Monotonic Lower Bounds and Thresholds
Wouter M. Koolen, Muriel Felipe Pérez-Ortiz, Tyron Lardy
Essentially all anytime-valid methods hinge on Ville's inequality to gain validity across time without incurring a union bound. Ville's inequality is a proper generalisation of Mar…
math.ST2025
Supermartingales for One-Sided Tests: Sufficient Monotone Likelihood Ratios are Sufficient
Peter D. Grünwald, Wouter M. Koolen
The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic…