Second Order Hadamard Differentiability in Statistical Applications

Jian-Jian Ren and Pranab Kumar Sen

Journal of Multivariate Analysis, 2001, vol. 77, issue 2, 187-228

Abstract: A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are established. These results are applied to derive the limiting distributions of a class of generalized Cramér-von Mises type test statistics, which include some proposed new ones for the tests of goodness of fit in the 3-sample problems, the tests in linear regression models, and the tests of bivariate independence, as special cases.

Keywords: Cramer-von; Mises; statistic; goodness; of; fit; test; Hadamard; differentiability; limiting; distribution; linear; models; M-estimator; statistical; functionals; uniform; asymptotic; linearity; weighted; empirical; processes (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (3)

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