p-value peeking and estimating extrema

TL;DR

This paper addresses the bias introduced by data peeking in statistical hypothesis testing by developing methods to estimate the true extrema of test statistics, improving the accuracy of p-values.

Contribution

It introduces principled mechanisms to estimate running extrema of test statistics, directly tackling the bias caused by peeking in various scenarios.

Findings

Methods effectively estimate true extrema despite peeking.

Approach reduces bias in p-value reporting.

Applicable to multiple testing scenarios.

Abstract

A pervasive issue in statistical hypothesis testing is that the reported $p$-values are biased downward by data "peeking" -- the practice of reporting only progressively extreme values of the test statistic as more data samples are collected. We develop principled mechanisms to estimate such running extrema of test statistics, which directly address the effect of peeking in some general scenarios.