Before revision:  Our approach  exploits the probability integral transform and relies on permuting estimated ``ranks'' instead of regression residuals. Unlike residuals, these ranks  are independent of the covariates, which allows us to establish the conditional validity of the resulting prediction intervals under consistent estimation of the conditional distributions.
After revision:  Our approach exploits the probability integral transform and relies on permuting estimated ranks are independent of the covariates, which allows us to establish the conditional validity of the resulting prediction intervals under consistent estimation of the conditional distributions.