Inference for Monotone Functions Under Short- and Long-Range Dependence: Confidence Intervals and New Universal Limits

• 成果类型: Article
• 署名作者: Bagchi, Pramita; Banerjee, Moulinath; Stoev, Stilian A.
• 署名单位: Ruhr University Bochum; University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1100622
• 发表日期: 2016
• 页码: 1634-1647
• 关键词: regression; CONVERGENCE; estimators; parameter; TRENDS

摘要

We introduce new point-wise confidence interval estimates for monotone functions observed with additive, dependent noise. Our methodology applies to both short- and long-range dependence regimes for the errors. The interval estimates are obtained via the method of inversion of certain discrepancy statistics. This approach avoids the estimation of nuisance parameters such as the derivative of the unknown function, which previous methods are forced to deal with. The resulting estimates are therefore more accurate, stable, and widely applicable in practice under minimal assumptions on the trend and error structure. The dependence of the errors especially long-range dependence leads to new phenomena, where new universal limits based on convex minorant functionals of drifted fractional Brownian motion emerge. Some extensions to uniform confidence bands are also developed. Supplementary materials for this article are available online.