Selective inference with a randomized response

Abstract

Inspired by sample splitting and the reusable holdout introduced in the field of differential privacy, we consider selective inference with a randomized response. We discuss two major advantages of using a randomized response for model selection. First, the selectively valid tests are more powerful after randomized selection. Second, it allows consistent estimation and weak convergence of selective inference procedures. Under independent sampling, we prove a selective (or privatized) central limit theorem that transfers procedures valid under asymptotic normality without selection to their corresponding selective counterparts. This allows selective inference in nonparametric settings. Finally, we propose a framework of inference after combining multiple randomized selection procedures. We focus on the classical asymptotic setting, leaving the interesting high-dimensional asymptotic questions for future work.

References in corpus (4)

• Exact and asymptotically robust permutation tests
• Selective inference with unknown variance via the square-root LASSO
• MAGIC: a general, powerful and tractable method for selective inference
• Asymptotics of selective inference

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• Inference After Selecting Plausibly Valid Instruments with Application to Mendelian Randomization
• Test Error Estimation after Model Selection Using Validation Error
• Analysis of error control in large scale two-stage multiple hypothesis testing
• Selection-adjusted inference: an application to confidence intervals for cis-eQTL effect sizes
• Scalable methods for Bayesian selective inference
• A general framework for estimation and inference from clusters of features