ADAPTIVE ESTIMATION OF THE SPARSITY IN THE GAUSSIAN VECTOR MODEL

• 成果类型: Article
• 署名作者: Carpentier, Alexandra; Verzelen, Nicolas
• 署名单位: Otto von Guericke University; INRAE; Institut Agro; Montpellier SupAgro; Universite de Montpellier
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1680
• 发表日期: 2019
• 页码: 93-126
• 关键词: higher criticism; null hypotheses; confidence sets; Minimax Rates; PROPORTION

摘要

Consider the Gaussian vector model with mean value.. We study the twin problems of estimating the number parallel to theta parallel to(0) of nonzero components of. and testing whether parallel to theta parallel to(0) is smaller than some value. For testing, we establish the minimax separation distances for this model and introduce a minimax adaptive test. Extensions to the case of unknown variance are also discussed. Rewriting the estimation of parallel to theta parallel to(0) as a multiple testing problem of all hypotheses {parallel to theta parallel to(0) <= q}, we both derive a new way of assessing the optimality of a sparsity estimator and we exhibit such an optimal procedure. This general approach provides a roadmap for estimating the complexity of the signal in various statistical models.