Asymptotics of Selective Inference

By Xiaoying Tian, Jonathan E. Taylor. 2015

71 citations recorded by the source corpus.

In this paper, we seek to establish asymptotic results for selective inference procedures removing the assumption of Gaussianity. The class of selection procedures we consider are determined by affine inequalities, which we refer to as affine selection procedures. Examples of affine selection procedures include selective inference along the solution path of the least absolute shrinkage and selection operator (LASSO), as well as selective inference after fitting the least absolute shrinkage and selection operator at a fixed value of the regularization parameter. We also consider some tests in penalized generalized linear models. Our result proves asymptotic convergence in the high‐dimensional setting where n

Subfields: Computational Mechanics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0f74aac5679b330d68a5da31e607092ae895a23d

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In Computational Mechanics

In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Selective inference with a randomized response (2015, background): “In the saturated model, our result provides a finer measure of convergence than in Tian and Taylor (2015).”
Optimal Inference After Model Selection (2014, methodology): “ck the robustness of data carving, we replace the Gaussian errors with independent errors drawn from Student’s tdistribution with ve degrees of freedom. The numbers barely change at all; see Table 2. Tian and Taylor (2017) rigorously analyze the case of non-Gaussian errors. 8 Conditioning as a Devic”
Exact post-selection inference for the generalized lasso path (2018, methodology): “Asymptotics for non-Gaussian error distributions are presented in Tian and Taylor [33], Tibshirani et al. [36].”
More powerful post-selection inference, with application to the Lasso (2018, background): “In the regime where p is fixed and n is growing, these assumptions can be dispensed with: • Tibshirani et al. (2014), Tian & Taylor (2017) show that the truncated normal pivot underlying the TZMs method holds asymptotically for a wide class of (non-normal) error distributions.”