Selective inference with a randomized response

By Xiaoying Tian, Jonathan E. Taylor. 2015

166 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/13594c3d461984009c5464179b89637bb691e964

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Citations in the corpus

Why adaptively collected data have negative bias and how to correct for it (2017, methodology): “We build upon results from recent developments in this area [22, 21, 11].”
Bootstrapping and sample splitting for high-dimensional, assumption-lean inference (2016, background): “Further works in this area include [69], [67], [42], [44], [68], [45].”
Exact post-selection inference for the generalized lasso path (2018, methodology): “An improvement based on auxiliary randomization is given in Tian and Taylor [34].”
More powerful post-selection inference, with application to the Lasso (2018, methodology): “• Tian & Taylor (2015) and Markovic et al. (2017) show that if an estimator of σ2 is consistent unconditionally, then it remains consistent conditional on selection (by the lasso).”
Distribution-Free Predictive Inference for Regression (2016, background): “In the second class, post-selection approaches, the focus is on covering coefficients in the best linear approximation to μ given a subset of selected covariates (see, e.g., Berk et al. 2013; Fithian, Sun, and Taylor 2014; Tian and Taylor 2017, 2018; Lee et al. 2016; Tibshirani et al. 2016).”
Splitting strategies for post-selection inference (2021, methodology): “To ensure high inferential power, Tian and Taylor (2018) recommend that the distribution of W has tails at least as heavy as the normal distribution.”