Empirical Bayes deconvolution estimates

• 成果类型: Article
• 署名作者: Efron, Bradley
• 署名单位: Stanford University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv068
• 发表日期: 2016
• 页码: 120
• 关键词: optimal rates; CONVERGENCE

摘要

An unknown prior density g(theta) has yielded realizations Theta(1), ..., Theta(N.) They are unobservable, but each i produces an observable value Xi according to a known probability mechanism, such as Xi similar to Po(Theta(i)). We wish to estimate g(theta) from the observed sample X-1, ..., X-N. Traditional asymptotic calculations are discouraging, indicating very slow nonparametric rates of convergence. In this article we show that parametric exponential family modelling of g(theta) can give useful estimates in moderate-sized samples. We illustrate the approach with a variety of real and artificial examples. Covariate information can be incorporated into the deconvolution process, leading to a more detailed theory of generalized linear mixed models.