Distribution free testing for linear regression. Extension to general parametric regression

Abstract

Recently a distribution free approach for testing parametric hypotheses based on unitary transformations has been suggested in Khmaladze [ , 2016Khmaladze [ , 2017 and further studied in Nguyen [2017] and Roberts [2019]. In this note we show that the transformation takes extremely simple form in distribution free testing of linear regression. Then we extend it to general parametric regression with vector-valued covariates.