Abstract
Complex studies involve many steps. Selecting promising findings based on pilot data is a first step. As more observations are collected, the investigator must decide how to combine the new data with the pilot data to construct valid selective inference. Carving, introduced by Fithian, Sun and Taylor (2014), enables the reuse of pilot data during selective inference and accounts for overoptimism from the selection process. However, currently, carving is only justified for parametric models such as the commonly used Gaussian model. In this paper, we develop the asymptotic theory to substantiate the use of carving beyond Gaussian models. Our results indicate that carving produces valid and tight confidence intervals within a model-free setting, as demonstrated through simulated and real instances.
Funding Statement
S.P. acknowledges support in part by NSF Grants DMS-1951980 and DMS-2113342.
Acknowledgments
S.P. would like to thank Jonathan Taylor, Liza Levina, Xuming He and two anonymous referees for providing several insightful comments on an initial draft of the paper.
Citation
Snigdha Panigrahi. "Carving model-free inference." Ann. Statist. 51 (6) 2318 - 2341, December 2023. https://doi.org/10.1214/23-AOS2318
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