Von Mises Calculus for Statistical Functionals

Fernholz, L T

ISBN 10: 0387908994 / ISBN 13: 9780387908991

Published by Springer, New York, NY, 1983

About this Item

Trade paperback (US). Glued binding. 124 p. Lecture Notes in Statistics, 19. Audience: General/trade. Very good. light shelfwear, previous owner name on first page,

Seller Inventory # Alibris.0028402

Bibliographic Details

• Title: Von Mises Calculus for Statistical Functionals
• Publisher: Springer, New York, NY
• Publication Date: 1983
• Language: English
• ISBN 10: 0387908994
• ISBN 13: 9780387908991
• Binding: Trade paperback

About this title

Synopsis

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.