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December 2016 Nonparametric estimation of dynamics of monotone trajectories
Debashis Paul, Jie Peng, Prabir Burman
Ann. Statist. 44(6): 2401-2432 (December 2016). DOI: 10.1214/15-AOS1409


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.


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Debashis Paul. Jie Peng. Prabir Burman. "Nonparametric estimation of dynamics of monotone trajectories." Ann. Statist. 44 (6) 2401 - 2432, December 2016.


Received: 1 January 2015; Revised: 1 October 2015; Published: December 2016
First available in Project Euclid: 23 November 2016

zbMATH: 1360.62190
MathSciNet: MR3576549
Digital Object Identifier: 10.1214/15-AOS1409

Primary: 62G08
Secondary: 62G20

Keywords: Autonomous differential equation , monotone trajectory , Nonlinear inverse problem , nonparametric estimation , Perturbation theory , Spline

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 6 • December 2016
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