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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Von Mises Calculus for Statistical Functionals

Von Mises Calculus for Statistical Functionals

Fernholz, L. T.

Paperback

Series: Lecture Notes in Statistics, Book 19

General MathematicsProbability & Statistics

ISBN10: 0387908994
ISBN13: 9780387908991
Publisher: Springer Nature
Published: Aug 29 1983
Pages: 124
Weight: 0.44
Height: 0.29 Width: 6.14 Depth: 9.21
Language: English
About forty years ago, Richard von Mises proposed a theory for the analysis of the asymptotic behavior of nonlinear statistical functionals based on the differentiability properties of these functionals. His theory was largely neglected until the late 1960's when it experienced a renaissance due to developments in the field of robust statistics. In particular, the Volterra derivative used by von Mises evolved into the influence curve, which was used to provide information about the sensi- ti vity of an estimator to outliers, as well as the estimator's asymptot- ic variance. Moreover, with the Princeton Robustness Study (Andrews et al. (1972)), there began a proliferation of new robust statistics, and the formal von Mises calculations provided a convenient heuristic tool for the analysis of the asymptotic distributions of these statistics. In the last few years, these calculations have been put in a more rigorous setting based on the Frechet and Hadamard, or compact, derivatives. The purpose of these notes is to provide von Mises' theory with a rig- orous mathematical framework which is sufficiently straightforward so that it can be applied routinely with little more effort than is required for the calculation of the influence curve. The approach presented here is based on the Hadamard derivative and is applicable to diverse forms of sta- tistical functionals.

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