The behavior of the npmle of a decreasing density near the boundaries of the support

• 成果类型: Article
• 署名作者: Kulikov, Vladimir N.; Lopuhaa, Hendrik P.
• 署名单位: Delft University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000100
• 发表日期: 2006
• 页码: 742-768
• 关键词: Asymptotic Normality; grenander-estimator; sample; error

摘要

We investigate the behavior of the nonparametric maximum likelihood estimator (f) over cap (n), for a decreasing density f near the boundaries of the support of f. We establish the limiting distribution of (f) over capn(n(-alpha)), where we need to distinguish between different values of 0 < alpha < 1. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of f at the boundaries of the support. The limit distribution of these estimators is established and their performance is compared with the penalized maximum likelihood estimator.