Selective inference with a randomized response
The authors investigate general selective inference with randomized response in model selection. They introduce the selective likelihood ratio and a framework of asymptotic analysis for selective models. The problems of consistent estimation and week convergence are studied. It is shown that randomization selection schemes lead to an increase in test powers. Linear regression models are used as examples. It is shown that the central limit theorem holds true under mild conditions on the selective distributions. This makes it possible to develop asymptotic selective inference in nonparametric settings. Finally, the paper discusses two extensions to multiple randomized selections: selective inference after cross-validation for LASSO and collaborative selective inference. Some additional sampling schemes and all proofs are given in the supplementary materials.
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