Asymptotically optimal inference in sparse sequence models with a simple data-dependent measure

2021/01/08 by Ryan Martin, Martin, Ryan
Decision Sciences · Engineering · Mathematics · #Control Systems and Identification #FOS: Mathematics #Probabilistic and Robust Engineering Design #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.2101.02983

Comments welcome at https://researchers.one/articles/21.01.00001

arxiv created 2021/01/08 · openalex publication_date 2021/01/08 · arxiv updated 2021/01/11 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28

Abstract

For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other hand, procedures should be computationally efficient and able to scale to very high dimensions. In this note, I show that a very simple data-dependent measure can achieve all of these desirable properties simultaneously, along with some robustness to the error distribution, in sparse sequence models.

Citations

• Estimation of the Mean of a Multivariate Normal Distribution
• Stein's Estimation Rule and its Competitors—An Empirical Bayes Approach
• The horseshoe estimator for sparse signals
• Adapting to unknown sparsity by controlling the false discovery rate

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