2014/05/13 by Stephen Reid, Reid, Stephen, Jonathan Taylor +3
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1405.3340
openalex publication_date 2014/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We tackle the problem of the estimation of a vector of means from a single\nvector-valued observation y. Whereas previous work reduces the size of the\nestimates for the largest (absolute) sample elements via shrinkage (like\nJames-Stein) or biases estimated via empirical Bayes methodology, we take a\nnovel approach. We adapt recent developments by Lee et al (2013) in post\nselection inference for the Lasso to the orthogonal setting, where sample\nelements have different underlying signal sizes. This is exactly the setup\nencountered when estimating many means. It is shown that other selection\nprocedures, like selecting the K largest (absolute) sample elements and the\nBenjamini-Hochberg procedure, can be cast into their framework, allowing us to\nleverage their results. Point and interval estimates for signal sizes are\nproposed. These seem to perform quite well against competitors, both recent and\nmore tenured.\n Furthermore, we prove an upper bound to the worst case risk of our estimator,\nwhen combined with the Benjamini-Hochberg procedure, and show that it is within\na constant multiple of the minimax risk over a rich set of parameter spaces\nmeant to evoke sparsity.\n