Adaptive Estimation of Nonparametric Functionals
Statistics Theory
2021-06-07 v5 Statistics Theory
Abstract
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals for which the theory produces rate optimally matching adaptive upper and lower bounds. Our results are automatically adaptive in both parametric and nonparametric regimes of estimation and are automatically adaptive and semiparametric efficient in the regime of parametric convergence rate.
Cite
@article{arxiv.1608.01364,
title = {Adaptive Estimation of Nonparametric Functionals},
author = {Lin Liu and Rajarshi Mukherjee and James Robins and Eric Tchetgen Tchetgen},
journal= {arXiv preprint arXiv:1608.01364},
year = {2021}
}
Comments
61 pages, polished writing and added some discussion on numerical issues of wavelets and potential connections to deep neural networks