regMMD: an R package for parametric estimation and regression with maximum mean discrepancy

This document provides a complete introduction to the template based on the regMMD package for R, that implements minimum distance estimation in various parametric and regression models using the maximum mean discrepancy (MMD) metric.

Authors

• Pierre Alquier (ESSEC Business School)
• Mathieu Gerber (University of Bristol)

Abstract

The Maximum Mean Discrepancy (MMD) is a kernel-based metric widely used for nonparametric tests and estimation. Recently, it has also been studied as an objective function for parametric estimation, as it has been shown to yield robust estimators. We have implemented MMD minimization for parameter inference in a wide range of statistical models, including various regression models, within an R package called regMMD. This paper provides an introduction to the regMMD package. We describe the available kernels and optimization procedures, as well as the default settings. Detailed applications to simulated and real data are provided.