Qihui Chen, Zheng Fang, Ruixuan Liu
arXiv 10 Dec 2025 · Econometrics
arXiv:2512.09257 · PDF · DOI · OpenAlex · Extracted main text
There has been significant progress in Bayesian inference based on sparsity-inducing (e.g., spike-and-slab and horseshoe-type) priors for high-dimensional regression models. The resulting posteriors, however, in general do not possess desirable frequentist properties, and the credible sets thus cannot serve as valid confidence sets even asymptotically. We introduce a novel debiasing approach that corrects the bias for the entire Bayesian posterior distribution. We establish a new Bernstein-von Mises theorem that guarantees the frequentist validity of the debiased posterior. We demonstrate the practical performance of our proposal through Monte Carlo simulations and two empirical applications in economics.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ray, Kolyan and Szabó, Botond (2022) Variational Bayes for high-dimensional linear regression with sparse priors | 0.971 | 12 | 5 | 92% |
| 2 | Castillo, I. and Schmidt-Hieber, J. and Van der Vaart, A (2015) Bayesian linear regression with sparse priors | 0.916 | 13 | 4 | 77% |
| 3 | van de Geer, S. and Bühlmann, P. and Ritov, Y.A. and Dezeure, R (2014) On asymptotically optimal confidence regions and tests for high-dimensional models | 0.885 | 13 | 5 | 69% |
| 4 | Bai, R. and Moran, G. E. and Antonelli, J. L. and Chen, Y. and Bolan… (2022) Spike-and-slab group lassos for grouped regression and sparse generalized additive models | 0.737 | 3 | 2 | 100% |
| 5 | Yiu, Andrew and Fong, Edwin and Holmes, Chris and Rousseau, Judith (2025) Semiparametric posterior corrections | 0.737 | 3 | 2 | 100% |
| 6 | Dezeure,R. and Bühlmann, P. and Meier, L. and Meinshausen, N (2015) High-Dimensional Inference: Confidence Intervals, p-values and R-Software hdi | 0.644 | 2 | 2 | 100% |
| 7 | Giannone, Domenico and Lenza, Michele and Primiceri, Giorgio E (2021) Economic predictions with big data: The illusion of sparsity | 0.644 | 2 | 2 | 100% |
| 8 | Rubin, D.B (1981) The Bayesian Bootstrap | 0.644 | 2 | 2 | 100% |
| 9 | Zhang, Cun-Hui and Zhang, Stephanie S (2014) Confidence intervals for low dimensional parameters in high dimensional linear models | 0.644 | 2 | 2 | 100% |
| 10 | Song, Q. and Liang, F (2023) Nearly optimal Bayesian shrinkage for high-dimensional regression | 0.630 | 8 | 3 | 25% |
Showing the top 10 of 56 scored citations.