arXiv 22 Apr 2022 · Econometrics
arXiv:2204.10495 · PDF · DOI · OpenAlex · Extracted main text
We develop an asymptotic theory of adversarial estimators ('A-estimators'). They generalize maximum-likelihood-type estimators ('M-estimators') as their average objective is maximized by some parameters and minimized by others. This class subsumes the continuous-updating Generalized Method of Moments, Generative Adversarial Networks and more recent proposals in machine learning and econometrics. In these examples, researchers state which aspects of the problem may in principle be used for estimation, and an adversary learns how to emphasize them optimally. We derive the convergence rates of A-estimators under pointwise and partial identification, and the normality of functionals of their parameters. Unknown functions may be approximated via sieves such as deep neural networks, for which we provide simplified low-level conditions. As a corollary, we obtain the normality of neural-net M-estimators, overcoming technical issues previously identified by the literature. Our theory yields novel results about a variety of A-estimators, providing intuition and formal justification for their success in recent applications.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Nishanth Dikkala, Greg Lewis, Lester Mackey, and Vasilis Syrgkanis (2020) Minimax estimation of conditional moment models | 1.000 | 10 | 4 | 100% |
| 2 | Victor Chernozhukov, Whitney Newey, Rahul Singh, and Vasilis Syrgkanis (2020) Adversarial estimation of riesz representers, 2020 | 1.000 | 8 | 3 | 100% |
| 3 | Bo Dai, Albert Shaw, Lihong Li, Lin Xiao, Niao He, Jianshu Chen, and… Sbeed: Convergent reinforcement learning with nonlinear function approximation | 1.000 | 7 | 3 | 100% |
| 4 | Andrew Bennett and Nathan Kallus (2012) The variational method of moments | 1.000 | 6 | 3 | 100% |
| 5 | Chunrong Ai and Xiaohong Chen Efficient estimation of models with conditional moment restrictions containing unknown functions | 0.928 | 4 | 3 | 100% |
| 6 | Whitney K. Newey and Richard J. Smith (2004) Higher order properties of gmm and generalized empirical likelihood estimators | 0.928 | 4 | 3 | 100% |
| 7 | Lars Peter Hansen (1982) Large sample properties of generalized method of moments estimators | 0.843 | 3 | 3 | 100% |
| 8 | Guido W. Imbens, Richard H. Spady, and Phillip Johnson (1998) Information theoretic approaches to inference in moment condition models | 0.843 | 3 | 3 | 100% |
| 9 | Xiaoxi Shen, Chang Jiang, Lyudmila Sakhanenko, and Qing Lu (2019) Asymptotic properties of neural network sieve estimators | 0.811 | 4 | 2 | 100% |
| 10 | Ryumei Nakada and Masaaki Imaizumi (2020) Adaptive approximation and generalization of deep neural network with intrinsic dimensionality | 0.737 | 4 | 4 | 50% |
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