# Notes on: Chwialkowski, K., Strathmann, H., & Gretton, A. (2016): A kernel test of goodness of fit

## Table of Contents

## Notation

- is the RKHS of real-valued functions on with reproducing kernel
- the product RKHS consisting of elements with , and standard inner product
- is rv. distributed according to measure
- is rv. distributed according to the
*target*measure

## Test Definition: Statistic and Threshold

### Defining Stein operator on RKHS

Define the Stein operator acting on

Operator can be expressed using the function:

whose expected inner product wiht vies expected value of the Stein operator:

where is the i-th component of .

Stein discrepancy in the RKHS:

### Wild Boostrap Testing

- Method for estimating the squared Stein discrepancy from samples