arXiv 21 Mar 2026 · Econometrics
arXiv:2603.20936 · PDF · OpenAlex · Extracted main text
The Riesz representer is a central object in semiparametric statistics and debiased/doubly-robust estimation. Two literatures in econometrics have highlighted the role for directly estimating Riesz representers: the automatic debiased machine learning literature (as in Chernozhukov et al., 2022b), and an independent literature on sieve methods for conditional moment models (as in Chen et al., 2014). These two literatures solve distinct optimization problems that in the population both have the Riesz representer as their solution. We show that with unregularized or ridge-regularized linear, sieve, or RKHS models, the two resulting estimators are numerically equivalent. However, for other regularization schemes such as the Lasso, or more general machine learning function classes including neural networks, the estimators are not necessarily equivalent. In the latter case, the Chen et al. (2014) formulation yields a novel constrained optimization problem for directly estimating Riesz representers with machine learning. Drawing on results from Birrell et al. (2022), we conjecture that this approach may offer statistical advantages at the cost of greater computational complexity.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chen, Xiaohong and Liao, Zhipeng and Sun, Yixiao (2014) Sieve inference on possibly misspecified semi-nonparametric time series models | 1.000 | 12 | 5 | 100% |
| 2 | Chernozhukov, Victor and Newey, Whitney K and Singh, Rahul (2022) Automatic debiased machine learning of causal and structural effects | 1.000 | 8 | 5 | 100% |
| 3 | Chen, Xiaohong and Pouzo, Demian (2015) Sieve Wald and QLR inferences on semi/nonparametric conditional moment models | 0.928 | 4 | 4 | 100% |
| 4 | Birrell, Jeremiah and Katsoulakis, Markos A and Pantazis, Yannis (2022) Optimizing variational representations of divergences and accelerating their statistical estimation | 0.928 | 4 | 3 | 100% |
| 5 | Kanamori, Takafumi and Hido, Shohei and Sugiyama, Masashi (2008) Efficient direct density ratio estimation for non-stationarity adaptation and outlier detection | 0.737 | 3 | 2 | 100% |
| 6 | Bruns-Smith, David and Dukes, Oliver and Feller, Avi and Ogburn, Eli… (2025) Augmented balancing weights as linear regression self | 0.644 | 2 | 2 | 100% |
| 7 | Chen, Xiaohong and Hong, Han and Tamer, Elie (2005) Measurement error models with auxiliary data | 0.644 | 2 | 2 | 100% |
| 8 | Lee, Kaitlyn J and Schuler, Alejandro (2025) RieszBoost: Gradient Boosting for Riesz Regression | 0.644 | 2 | 2 | 100% |
| 9 | Sugiyama, Masashi and Takeuchi, Ichiro and Suzuki, Taiji and Kanamor… (2010) Conditional density estimation via least-squares density ratio estimation | 0.644 | 2 | 2 | 100% |
| 10 | Ai, Chunrong and Chen, Xiaohong (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions | 0.405 | 1 | 1 | 100% |
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