Titlebook: Contributions to a General Asymptotic Statistical Theory; J. Pfanzagl Book 1982 Springer-Verlag, New York Inc. 1982 Asymptotische Wirksamk

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V. A. Tverdislov,E. N. Gerasimovaκ — κ (P)) cannot be more concentrated about 0 than N(O,P(κ (·,P).)). Hence it is justified to call an estimator- sequence which is as. median unbiased for κ on β, .. . for κ on β if it is as. normal with variance P(κ (·,P).).

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Cases Illustrating the Variation of ResultsFor many families of p-measures occurring in the literature the tangent cones are, in fact, linear spaces. This chapter contains some examples of this kind. Several families do, however, not share all of the additional properties discussed in Chapter 1, such as loc. as. symmetry or loc. as. convexity.

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E. W. Jecht,R. Müller,E. ZieglwalnerLet κ: β → IR be a functional. For asymptotic theory, the . . of this functional are essential, i.e., its behavior in contiguous neighborhoods. These local properties determine how good optimal tests and estimators can be asymptotically. The mathematical construct suitable for this purpose is the gradient.

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https://doi.org/10.1007/978-3-642-68263-6Let (x, .) be a measurable space and k: x.→ IR a measurable function. For a p-measure P |. the . is defined by κ(P):= ∫k(x.,…,x )P(dx.)…P(dx.). Many widely used functionals are of this type:

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