Second order Hadamard differentiability in statistical applications

A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are establishe d. These results are applied to derive the limiting distributions of a clas s of generalized Cramer-von Mises type test statistics, which include some proposed neu ones for the tests or goodness of fit in the 3-sample problems . the tests in linear regression models. and the tests uf bivariate indepen dence as special cases. (C) 2001 Academic Press.