In a parametric counterpart of the nonparametric considerations of Neuhaus, a class of quadratic goodness of fit statistics is developed generalizing the usual Cramer-von Mises statistics.
"Addendum to: "Local Asymptotics for Linear Rank Statistics with Estimated Score Functions"." Ann. Statist. 16 (3) 1342 - 1343, September, 1988. https://doi.org/10.1214/aos/1176350967