# Hypothesis testing for matched pairs with missing data by maximum mean discrepancy: An application to continuous glucose monitoring

arXiv: https://arxiv.org/abs/2206.01590 · HTML: https://mlsanity.com/paper/2206.01590/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 73 references that are in the map.
- First posted on arXiv 3 Jun 2022.

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

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Robust Inference Using Inverse Probability Weighting](https://mlsanity.com/paper/1810.11397/) (2018)
- [Functional Models for Time-Varying Random Objects](https://mlsanity.com/paper/1907.10829/) (2019)
- [Distributional data analysis of accelerometer data from the NHANES database using nonparametric survey regression models](https://mlsanity.com/paper/2104.01165/) (2021)
- [Kernel k-Groups via Hartigan's Method](https://mlsanity.com/paper/1710.09859/) (2017)
- [A maximum-mean-discrepancy goodness-of-fit test for censored data](https://mlsanity.com/paper/1810.04286/) (2018)
- [Wasserstein F-tests and Confidence Bands for the Fr`echet Regression of Density Response Curves](https://mlsanity.com/paper/1910.13418/) (2019)
- [The Exact Equivalence of Distance and Kernel Methods for Hypothesis Testing](https://mlsanity.com/paper/1806.05514/) (2018)
- [Distributional data analysis via quantile functions and its application to modelling digital biomarkers of gait in Alzheimer's Disease](https://mlsanity.com/paper/2102.10783/) (2021)
- [Asymptotic based bootstrap approach for matched pairs with missingness in a single-arm](https://mlsanity.com/paper/1912.04902/) (2019)
- [Testing Independence under Biased Sampling](https://mlsanity.com/paper/1912.05769/) (2019)

## Built on by (most cited first, 2 of 2)

- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Distributional Random Forests for Complex Survey Designs](https://mlsanity.com/paper/2512.08179/) (2025)

## Abstract (arXiv)

A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring biological systems raises the need for addressing more complex data, e.g., graphs, strings and probability distributions, among others. In order to fill this gap, this paper proposes new estimators of the maximum mean discrepancy (MMD) to handle complex matched pairs with missing data. These estimators can detect differences in data distributions under different missingness mechanisms. The validity of this approach is proven and further studied in an extensive simulation study, and results of statistical consistency are provided. Data from continuous glucose monitoring in a longitudinal population-based diabetes study are used to illustrate the application of this approach. By employing the new distributional representations together with cluster analysis, new clinical criteria on how glucose changes vary at the distributional level over five years can be explored.