Nonparametric estimation of dynamics of monotone trajectories
Debashis Paul, Jie Peng, Prabir Burman
The Annals of Statistics · 2016 · Volume 44 · Issue 6
Abstract
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.
Keywords
62G08, 62G20, Autonomous differential equation, monotone trajectory, Nonlinear inverse problem, nonparametric estimation, Perturbation theory, Spline
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