A Special Call for Contributed Discussions
Stat, the innovative electronic statistics journal and joint venture between the International Statistical Institute and Wiley, solicits discussions of the paper “A note on universal inference“, by Timmy Tse and Anthony Davison. Discussions should be between one and two pages. Discussants will have one month to prepare their discussion after accepting our invitation, except that all discussions must be submitted via the Wiley Authors Submission platform by 15 January 2023. Any rejoinder will be submitted by 15 February 2023.
The abstract is provided below:
Universal inference enables the construction of confidence intervals and tests without regularity conditions by splitting the data into two parts and appealing to Markov’s inequality. Previous investigations have shown that the cost of this generality is a loss of power in regular settings for testing simple hypotheses. The present paper makes three contributions. We first clarify the reasons for the loss of power, and use a simple illustrative example to investigate how the split proportion optimising the power depends on the nominal size of the test. We then show that the presence of nuisance parameters can severely impact the power, and suggest a simple asymptotic improvement. Finally we show that combining many data splits can also sharply diminish power.