Adaptive estimation of nonparametric functionals
Authors: Lin Liu, Rajarshi Mukherjee, James M. Robins, Eric Tchetgen Tchetgen
JMLR 2021 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | 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. ... Section 6, Appendices A, B, and C are devoted for the proofs of the theorems and collecting useful technical lemmas. |
| Researcher Affiliation | Academia | Lin Liu EMAIL 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 Rajarshi Mukherjee EMAIL Department of Biostatistics Harvard T. H. Chan School of Public Health Boston, MA 02115, USA James M. Robins EMAIL Department of Epidemiology and Department of Biostatistics Harvard T. H. Chan School of Public Health Boston, MA 02115, USA Eric Tchetgen Tchetgen EMAIL Wharton Statistics Department The University of Pennsylvania Philadelphia, PA 19104, USA |
| Pseudocode | No | The paper describes theoretical methods and mathematical proofs. It does not contain any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any specific statement about releasing code for the described methodology, nor does it include links to a code repository. The license information provided is for the paper itself, not for source code. |
| Open Datasets | No | The paper focuses on theoretical models and examples of functionals in nonparametric analyses (e.g., average treatment effect estimation, mean estimation in missing data studies). It does not describe experiments using specific datasets, nor does it provide any links or citations for publicly available datasets used in empirical validation. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments on datasets. While it discusses splitting a theoretical 'sample D into M disjoint subsamples', this refers to a theoretical sample splitting *scheme* for analysis, not concrete training/test/validation splits for empirical reproduction. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical proofs and adaptive estimation. It does not describe any computational experiments, and therefore, no hardware specifications are provided. |
| Software Dependencies | No | The paper is theoretical. While it mentions 'wavelet kernel projections' as a mathematical tool, it does not specify any software names with version numbers or libraries used for computational implementation or experiments. |
| Experiment Setup | No | The paper presents theoretical work on adaptive estimation of nonparametric functionals. It does not include any experimental setup details such as hyperparameters, training configurations, or system-level settings, as no empirical experiments are described. |