Carving model-free inference
The Annals of Statistics · 2023 · Volume 51 · Issue 6
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.
Keywords
62E20, 62G15, 62G20, carving, conditional inference, model-free, Post-selection inference, Randomization, selective inference
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