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.

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.