Carving model-free inference

Exploratory analyses mark a starting point for many scientific investigations, often carried out on pilot samples to find relevant parameters for downstream inference. With the availability of fresh samples, construction of effect-size estimates for these parameters is a standard goal in confirmatory analyses. Addressing the pitfalls of selection bias, a conditional perspective on inference-- via a data carved law-- offers an efficient way to reuse samples deployed during explorations. The principles of carving, in practice, apply very broadly to a wide range of generative schemes. Nonetheless, the theory for valid inference is strongly tied to parametric models; an example being the ubiquitous Gaussian model. The results in this paper support model-free carved inference in an asymptotic sense.