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.
"Testing conditional independence via Rosenblatt transforms." Ann. Statist. 37 (6B) 4011 - 4045, December 2009. https://doi.org/10.1214/09-AOS704