Improving point and interval estimators of monotone functions by rearrangement

• 成果类型: Article
• 署名作者: Chernozhukov, V.; Fernandez-Val, I.; Galichon, A.
• 署名单位: Massachusetts Institute of Technology (MIT); Boston University; Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asp030
• 发表日期: 2009
• 页码: 559575
• 关键词: Nonparametric regression; Asymptotic Normality; STRICTLY MONOTONE; series estimators; confidence bands; quantiles; splines

摘要

Suppose that a target function is monotonic and an available original estimate of this target function is not monotonic. Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function. Furthermore, suppose an original confidence interval, which covers the target function with probability at least 1-alpha, is defined by an upper and lower endpoint functions that are not monotonic. Then the rearranged confidence interval, defined by the rearranged upper and lower endpoint functions, is monotonic, shorter in length in common norms than the original interval, and covers the target function with probability at least 1-alpha. We illustrate the results with a growth chart example.