Adaptive estimation of nonparametric functionals

被引：0
|
作者：
Liu, Lin [1 ]
Mukherjee, Rajarshi [2 ]
Robins, James M. [3 ]
Tchetgen, Eric Tchetgen [4 ]
机构：
[1] Institute of Natural Sciences, MOE-LSC, School of Mathematical Sciences, SJTU-Yale Center for Biostatistics and Data Science, Shanghai Jiao Tong University, Shanghai,200240, China
[2] Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston,MA,02115, United States
[3] Department of Epidemiology and Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston,MA,02115, United States
[4] Wharton Statistics Department, The University of Pennsylvania, Philadelphia,PA,19104, United States
来源：
Journal of Machine Learning Research | 2021年 / 22卷
基金：
美国国家科学基金会; 中国国家自然科学基金; 美国国家卫生研究院;
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摘要：
We provide general adaptive upper bounds for estimating nonparametric functionals based on second-order U-statistics arising from finite-dimensional approximation of the infinitedimensional 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. © 2021 Microtome Publishing. All rights reserved.
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