# Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection

arXiv: https://arxiv.org/abs/2111.05277 · HTML: https://mlsanity.com/paper/2111.05277/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 58 references that are in the map.
- First posted on arXiv 9 Nov 2021.

## Builds on (most cited first, 11 of 11)

- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Generalized Optimal Matching Methods for Causal Inference](https://mlsanity.com/paper/1612.08321/) (2016)
- [Metrizing Weak Convergence with Maximum Mean Discrepancies](https://mlsanity.com/paper/2006.09268/) (2020)
- [De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers](https://mlsanity.com/paper/1802.08667/) (2018)
- [Counterfactual Mean Embeddings](https://mlsanity.com/paper/1805.08845/) (2018)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [Minimax Linear Estimation of the Retargeted Mean](https://mlsanity.com/paper/1901.10296/) (2019)
- [A Simple and General Debiased Machine Learning Theorem with Finite Sample Guarantees](https://mlsanity.com/paper/2105.15197/) (2021)
- [Double machine learning for sample selection models](https://mlsanity.com/paper/2012.00745/) (2020)

## Built on by (most cited first, 1 of 1)

- [Kernel methods for long term dose response curves](https://mlsanity.com/paper/2201.05139/) (2022)

## Abstract (arXiv)

I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select observations, the outcome is observed. I assume selection is as good as random conditional on treatment and a sufficiently rich set of observed covariates, where the covariates are allowed to cause treatment or be caused by treatment -- an extension of missingness-at-random (MAR). I propose estimators of means, increments, and distributions of counterfactual outcomes with closed form solutions in terms of kernel matrix operations, allowing treatment and covariates to be discrete or continuous, and low, high, or infinite dimensional. For the continuous treatment case, I prove uniform consistency with finite sample rates. For the discrete treatment case, I prove root-n consistency, Gaussian approximation, and semiparametric efficiency.