https://orcid.org/0000-0002-8568-440X
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Neil Dey, Ryan Martin, Jonathan P Williams, Neil Dey, Ryan Martin, and Jonathan P. Williams’ contribution to the Discussion of ‘Safe Testing’ by Grünwald, de Heide, and Koolen, Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 86, Issue 5, November 2024, Pages 1147–1148, https://doi.org/10.1093/jrsssb/qkae063
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Congratulations to Grünwald, de Heide, and Koolen (GHK) for their contribution to the exciting and rapidly growing literature on safe/anytime-valid inference. GHK’s proposal focused on problems in which a statistical model is available that determines the quantity of interest—the model parameter—and provides a likelihood function that drives the e-value construction. When data are observed and analysed sequentially, however, the data analyst typically cannot say with any certainty what statistical model might be appropriate. Our comments below focus on what can be done along the lines of safe/anytime-valid inference without a correctly specified statistical model.
Two recent developments deserve mention. First, Park, Balakrishnan, and Wasserman, in their recent arXiv paper (https://arxiv.org/abs/2307.04034) develop a version of the universal inference framework (Wasserman et al., 2020) that accommodates model misspecification but is not designed for the online setting. Second, the nonparametric approach in Waudby-Smith and Ramdas (2024) offers anytime-valid inference, but focuses exclusively on the mean of the data-generating process.
