A general class of recursive residuals is defined by means of lower-triangular, orthonormal transformations. For these residuals, some weak invariance principles are established under appropriate regularity conditions. The theory is then incorporated in the study of robustness of some tests for change of parameters occurring at unknown time points.
Pranab Kumar Sen. "Invariance Principles for Recursive Residuals." Ann. Statist. 10 (1) 307 - 312, March, 1982. https://doi.org/10.1214/aos/1176345714