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