Adaptive Estimation of Nonparametric Functionals
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
Text
Liu et al. "Adaptive Estimation of Nonparametric Functionals." Journal of Machine Learning Research, 2021.Markdown
[Liu et al. "Adaptive Estimation of Nonparametric Functionals." Journal of Machine Learning Research, 2021.](https://mlanthology.org/jmlr/2021/liu2021jmlr-adaptive/)BibTeX
@article{liu2021jmlr-adaptive,
title = {{Adaptive Estimation of Nonparametric Functionals}},
author = {Liu, Lin and Mukherjee, Rajarshi and Robins, James M. and Tchetgen, Eric Tchetgen},
journal = {Journal of Machine Learning Research},
year = {2021},
pages = {1-66},
volume = {22},
url = {https://mlanthology.org/jmlr/2021/liu2021jmlr-adaptive/}
}