NONPARAMETRIC ESTIMATION OF DYNAMICS OF MONOTONE TRAJECTORIES

• 成果类型: Article
• 署名作者: Paul, Debashis; Peng, Jie; Burman, Prabir
• 署名单位: University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1409
• 发表日期: 2016
• 页码: 2401-2432
• 关键词: time-varying coefficients; differential-equations; parameter-estimation; models; derivatives

摘要

We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity conditions, we show that in terms of L-2-loss, the optimal rate of convergence for the proposed estimator is the same as that for the estimation of the derivative of a function. We conduct simulation studies to examine the finite sample behavior of the proposed estimator and apply it to the Berkeley growth data.