December 2023 Carving model-free inference
Snigdha Panigrahi
Author Affiliations +
Ann. Statist. 51(6): 2318-2341 (December 2023). DOI: 10.1214/23-AOS2318


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.


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.


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Snigdha Panigrahi. "Carving model-free inference." Ann. Statist. 51 (6) 2318 - 2341, December 2023.


Received: 1 March 2022; Revised: 1 July 2023; Published: December 2023
First available in Project Euclid: 20 December 2023

MathSciNet: MR4682699
zbMATH: 07783617
Digital Object Identifier: 10.1214/23-AOS2318

Primary: 62E20
Secondary: 62G15 , 62G20

Keywords: carving , conditional inference , model-free , Post-selection inference , Randomization , selective inference

Rights: Copyright © 2023 Institute of Mathematical Statistics


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Vol.51 • No. 6 • December 2023
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