Abstract
Classically, a stastistical functional is defined on a space of distribution F on the real line with the supremum norn. The values may be real or themselves functions such as the quantile function \(F^{-1}\). Nonlinear functionals are studied via their derivatives. This paper and a related one [Dudley (1991a)] will show that the differentiability properties originally proved by Reeds (1976), also treated in Fernholz (1983), can be improved substantially.
Revised February 1991; revised October 1991.
Research partially supported by an NSF grant.
AMS 1980 subject classifications. Primary 60F17, 62G30; secondary 26A42, 26A45.
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Dudley, R.M. (2010). Fréchet Differentiability, p-Variation and Uniform Donsker Classes. In: Giné, E., Koltchinskii, V., Norvaisa, R. (eds) Selected Works of R.M. Dudley. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5821-1_21
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