# Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence

arXiv: https://arxiv.org/abs/1912.05737 · HTML: https://mlsanity.com/paper/1912.05737/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2019.

## Built on by (most cited first, 25 of 25)

- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
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- [Clustering Market Regimes using the Wasserstein Distance](https://mlsanity.com/paper/2110.11848/) (2021)
- [Efficient and Accurate Explanation Estimation with Distribution Compression](https://mlsanity.com/paper/2406.18334/) (2024)
- [Change Detection of Markov Kernels with Unknown Pre and Post Change Kernel](https://mlsanity.com/paper/2201.11722/) (2022)
- [A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networks](https://mlsanity.com/paper/2303.02637/) (2023)
- [Minimum Distance Summaries for Robust Neural Posterior Estimation](https://mlsanity.com/paper/2602.09161/) (2026)
- [Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structures](https://mlsanity.com/paper/2306.15835/) (2023)
- [Distributional Statistics Restore Training Data Auditability in One-step Distilled Diffusion Models](https://mlsanity.com/paper/2502.02970/) (2025)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [A Bayesian Non-parametric Approach to Generative Models: Integrating Variational Autoencoder and Generative Adversarial Networks using Wasserstein and Maximum Mean Discrepancy](https://mlsanity.com/paper/2308.14048/) (2023)
- [A Gradient Flow Perspective on Minimum MMD Estimation](https://mlsanity.com/paper/2607.03871/) (2026)
- [Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption](https://mlsanity.com/paper/2309.16409/) (2023)
- [Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Data](https://mlsanity.com/paper/2505.08698/) (2025)
- [Generalising maximum mean discrepancy: kernelised functional Bregman divergences](https://mlsanity.com/paper/2604.24047/) (2026)
- [Gaussian mixture models in Hilbert spaces via kernel methods](https://mlsanity.com/paper/2605.05996/) (2026)
- [Nonparametric Deconvolution and Denoising using Simulation Based Inference](https://mlsanity.com/paper/2606.21907/) (2026)
- [Markov Chain Convergence in Kernel-Induced Geometry](https://mlsanity.com/paper/2610.13916/) (2026)

## Abstract (arXiv)

Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this distribution. This question is of major interest, in particular because the universality property leads to the robustness of the estimator. In this paper, we tackle the problem of universal estimation using a minimum distance estimator presented in Briol et al. (2019) based on the Maximum Mean Discrepancy. We show that the estimator is robust to both dependence and to the presence of outliers in the dataset. Finally, we provide a theoretical study of the stochastic gradient descent algorithm used to compute the estimator, and we support our findings with numerical simulations. ** The proof of Proposition 4.4 in the published version contains a mistake. The mistake is fixed here (and the bound is actually improved by a factor 2). **