Determining the Correct Hierarchy of Reliability Standards in Frequentist Inference

Determine the correct hierarchy of reliability-based evaluative standards in frequentist statistics across problem contexts (e.g., admissibility, unbiasedness, uniformly minimum variance among unbiased estimators for estimation; low significance level, uniform most powerful tests for hypothesis testing), specifying which standards are higher or lower and under what conditions each should serve as the operative criterion.

Background

The paper develops an achievabilist version of reliabilism, proposing that in each context of inquiry the operative standard should be the highest achievable reliability criterion. Across tasks like hypothesis testing and point estimation, multiple standards are available (e.g., significance level, uniform most powerful, unbiasedness, admissibility, UMVU), and their relative status is not fully settled.

The author notes controversies (e.g., around unbiasedness) and explicitly states that identifying the correct hierarchy of these standards remains open and requires further exploration and debate.