Estimation of a two-component mixture model with applications to multiple testing

• 成果类型: Article
• 署名作者: Patra, Rohit Kumar; Sen, Bodhisattva
• 署名单位: Columbia University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12148
• 发表日期: 2016
• 页码: 869-893
• 关键词: true null hypotheses; false-discovery rate; adaptive-control; PROPORTION; number

摘要

We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution non-parametrically, given independent and identically distributed data from the mixture model, using ideas from shape-restricted function estimation. We establish the consistency of our estimators. We find the rate of convergence and asymptotic limit of the estimator for the mixing proportion. Completely automated distribution-free honest finite sample lower confidence bounds are developed for the mixing proportion. Connection to the problem of multiple testing is discussed. The identifiability of the model and the estimation of the density of the unknown distribution are also addressed. We compare the estimators proposed, which are easily implementable, with some of the existing procedures through simulation studies and analyse two data sets: one arising from an application in astronomy and the other from a microarray experiment.