# Orthogonal Series Estimation for the Ratio of Conditional Expectation Functions

arXiv: https://arxiv.org/abs/2212.13145 · HTML: https://mlsanity.com/paper/2212.13145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 70 references that are in the map.
- First posted on arXiv 26 Dec 2022.

## Builds on (most cited first, 17 of 17)

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- [Convergence rates of deep ReLU networks for multiclass classification](https://mlsanity.com/paper/2108.00969/) (2021)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [Asymptotic Distributions and Rates of Convergence for Random Forests via Generalized U-statistics](https://mlsanity.com/paper/1905.10651/) (2019)
- [Estimation and Inference with Trees and Forests in High Dimensions](https://mlsanity.com/paper/2007.03210/) (2020)
- [High-Dimensional L2Boosting: Rate of Convergence](https://mlsanity.com/paper/1602.08927/) (2016)
- [Efficient nonparametric causal inference with missing exposure information](https://mlsanity.com/paper/1802.08952/) (2018)
- [Uplift Modeling from Separate Labels](https://mlsanity.com/paper/1803.05112/) (2018)
- [Group Average Treatment Effects for Observational Studies](https://mlsanity.com/paper/1911.02688/) (2019)
- [Estimation and Validation of Ratio-based Conditional Average Treatment Effects Using Observational Data](https://mlsanity.com/paper/1912.06977/) (2019)
- [Relative Contrast Estimation and Inference for Treatment Recommendation](https://mlsanity.com/paper/2010.13904/) (2020)
- [Estimation of Local Average Treatment Effect by Data Combination](https://mlsanity.com/paper/2109.05175/) (2021)
- [Structural mean models for instrumented difference-in-differences](https://mlsanity.com/paper/2209.10339/) (2022)

## Abstract (arXiv)

In various fields of data science, researchers are often interested in estimating the ratio of conditional expectation functions (CEFR). Specifically in causal inference problems, it is sometimes natural to consider ratio-based treatment effects, such as odds ratios and hazard ratios, and even difference-based treatment effects are identified as CEFR in some empirically relevant settings. This chapter develops the general framework for estimation and inference on CEFR, which allows the use of flexible machine learning for infinite-dimensional nuisance parameters. In the first stage of the framework, the orthogonal signals are constructed using debiased machine learning techniques to mitigate the negative impacts of the regularization bias in the nuisance estimates on the target estimates. The signals are then combined with a novel series estimator tailored for CEFR. We derive the pointwise and uniform asymptotic results for estimation and inference on CEFR, including the validity of the Gaussian bootstrap, and provide low-level sufficient conditions to apply the proposed framework to some specific examples. We demonstrate the finite-sample performance of the series estimator constructed under the proposed framework by numerical simulations. Finally, we apply the proposed method to estimate the causal effect of the 401(k) program on household assets.