In this paper we study a marked empirical process based on residuals. Results on its large-sample behavior may be used to provide nonparametric full-model checks for regression. Their decomposition into principal components gives new insight into the question: which kind of departure from a hypothetical model may be well detected by residual-based goodness-of-fit methods? The work also contains a small simulation study on straight-line regression.
"Nonparametric model checks for regression." Ann. Statist. 25 (2) 613 - 641, April 1997. https://doi.org/10.1214/aos/1031833666