Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations

Understand

Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making.

• However, strong guarantees are limited to parametric sequential tests that under-cover in practice or concentration-bound-based sequences that over-cover and have suboptimal rejection times.
• In this work, we consider classic delayed-start normal-mixture sequential probability ratio tests, and we provide the first asymptotic type-I-error and expected-rejection-time guarantees under general non-parametric data generating processes, where the asymptotics are indexed by the test's burn-in time.
• The type-I-error results primarily leverage a martingale strong invariance principle and establish that these tests (and their implied confidence sequences) have type-I error rates asymptotically equivalent to the desired (possibly varying) $\alpha$-level.