# Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing data

arXiv: https://arxiv.org/abs/2107.07371 · HTML: https://mlsanity.com/paper/2107.07371/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 15 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [Combining multiple observational data sources to estimate causal effects](https://mlsanity.com/paper/1801.00802/) (2018)
- [A representer theorem for deep kernel learning](https://mlsanity.com/paper/1709.10441/) (2017)
- [Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data](https://mlsanity.com/paper/1710.08074/) (2017)
- [An Online Projection Estimator for Nonparametric Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2104.00780/) (2021)
- [Semiparametric fractional imputation using Gaussian mixture models for handling multivariate missing data](https://mlsanity.com/paper/1809.05976/) (2018)

## Built on by (most cited first, 3 of 3)

- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)
- [Minimum Wasserstein distance estimator under covariate shift: closed-form, super-efficiency and irregularity](https://mlsanity.com/paper/2601.07282/) (2026)
- [Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regression](https://mlsanity.com/paper/2602.18958/) (2026)

## Abstract (arXiv)

Imputation and propensity score weighting are two popular techniques for handling missing data. We address these problems using the regularized M-estimation techniques in the reproducing kernel Hilbert space. Specifically, we first use the kernel ridge regression to develop imputation for handling item nonresponse. While this nonparametric approach is potentially promising for imputation, its statistical properties are not investigated in the literature. Under some conditions on the order of the tuning parameter, we first establish the root-n consistency of the kernel ridge regression imputation estimator and show that it achieves the lower bound of the semiparametric asymptotic variance. A nonparametric propensity score estimator using the reproducing kernel Hilbert space is also developed by a novel application of the maximum entropy method for the density ratio function estimation. We show that the resulting propensity score estimator is asymptotically equivalent to the kernel ridge regression imputation estimator. Results from a limited simulation study are also presented to confirm our theory. The proposed method is applied to analyze the air pollution data measured in Beijing, China.