Titlebook: von Mises Calculus For Statistical Functionals; Luisa Turrin Fernholz Book 1983 Springer-Verlag New York Inc. 1983 Asymptotische Normalver

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,Von Mises’ Method,1977, 1981), and Serfling (1980). One result of these extensions is that the field has become divergent, with ad hoc techniques applied in different situations. In the chapters that follow we shall try to establish a unified methodology that can be applied to wide classes of statistics.

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Hadamard Differentiation,s, and prove an implicit function theorem which will later be applied to implicitly defined statistical functionals. More details on the topics covered here can be found in Averbukh and Smolyanov (1968), Yamamuro (1974), and Keller (1974).

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,Von Mises’ Method,c technique was introduced by von Mises (1947) and has been extended in various directions by several authors: Filippova (1962), Reeds (1976), Huber (1977, 1981), and Serfling (1980). One result of these extensions is that the field has become divergent, with ad hoc techniques applied in different s

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Hadamard Differentiation,r the study of these properties we present here some basic definitions and results on differentiation of functions defined on topological vector spaces, and prove an implicit function theorem which will later be applied to implicitly defined statistical functionals. More details on the topics covere

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Calculus on Function Spaces,this, we present here the rudiments of a calculus for functionals defined on D[0,1], which will enable us to deal with the statistical functionals that we considered in the last chapter, as well as others that we shall introduce later.

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Asymptotic Efficiency,oof that Fréchet differentiable functionals are asymptotically efficient if and only if the influence curve satisfies certain conditions. However he also noted that “the rather stringent regularity conditions — Fréchet differentiability — will rarely be satisfied”. Here we show that Huber’s result h