# Testing conditional independence via Rosenblatt transforms

## TL;DR

This paper introduces new distribution-free tests for conditional independence using Rosenblatt transforms, applicable to single-index models with unknown parameters, and demonstrates their effectiveness through Monte Carlo simulations.

## Contribution

It proposes novel tests based on Rosenblatt transforms for conditional independence in single-index models, maintaining distribution-freeness and computational simplicity.

## Key findings

- Tests are distribution-free under the null hypothesis.
- Monte Carlo simulations show good size and power properties.
- Method is computationally convenient for practical use.

## Abstract

This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while retaining computational convenience. Some results from Monte Carlo simulations are presented and discussed.

---
Source: https://tomesphere.com/paper/0911.3787