A general asymptotic scheme for inference under order restrictions

• 成果类型: Article
• 署名作者: Anevski, D.; Hossjer, O.
• 署名单位: Chalmers University of Technology; University of Gothenburg; Lund University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000443
• 发表日期: 2006
• 页码: 1874-1930
• 关键词: range dependent sequences; monotone regression; brownian-motion; Nonparametric Regression; Empirical Process; density; SUBORDINATION; CONVERGENCE; estimators; sums

摘要

Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, and estimation of monotone and convex density functions. Various pointwise limit distributions are obtained, and the rate of convergence depends on the self similarity properties and on the rate of convergence of the processes considered.