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 et al. (2014), enables the reuse of pilot data during selective inference and accounts for over-optimism from the selection process. Currently, the justification for carving is tied to parametric models, like the commonly used Gaussian model. In this paper, we develop the asymptotic theory to substantiate the use of carving beyond Gaussian models. Through both simulated and real instances, we find that carving produces valid and tight confidence intervals within a model-free setting.

翻译：复杂研究涉及多个步骤。基于初步数据筛选有前景的发现是第一步。随着更多观测数据的收集，研究者必须决定如何将新数据与初步数据结合以构建有效的选择性推论。Fithian等人（2014）提出的"雕琢"方法，允许在选择性推论中重复使用初步数据，并校正由选择过程导致的过度乐观偏差。目前，雕琢方法的理论合理性依赖于参数模型，如常用的高斯模型。本文发展了渐近理论，论证了雕琢方法在高斯模型之外的应用合理性。通过模拟实验和实际案例分析，我们发现雕琢方法能在无模型设定下生成有效且紧凑的置信区间。