# A Kernel Test of Goodness of Fit

arXiv: https://arxiv.org/abs/1602.02964 · HTML: https://mlsanity.com/paper/1602.02964/

## Key facts

- Cited by 143 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2016.

## Built on by (most cited first, 30 of 143)

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## Abstract (arXiv)

We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence constructed via Stein's method using functions from a Reproducing Kernel Hilbert Space. Our test statistic is based on an empirical estimate of this divergence, taking the form of a V-statistic in terms of the log gradients of the target density and the kernel. We derive a statistical test, both for i.i.d. and non-i.i.d. samples, where we estimate the null distribution quantiles using a wild bootstrap procedure. We apply our test to quantifying convergence of approximate Markov Chain Monte Carlo methods, statistical model criticism, and evaluating quality of fit vs model complexity in nonparametric density estimation.