Abstract
In this chapter we show that Hadamard differentiability can be used to prove asymptotic efficiency for statistical functionals. Huber (1977) gave a proof 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 holds under the weaker assumption of Hadamard differentiability. Since we have shown that several classes of statistical functionals are Hadamard differentiable, this approach to asymptotic efficiency through Hadamard differentiability has wide applicability.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Fernholz, L.T. (1983). Asymptotic Efficiency. In: von Mises Calculus For Statistical Functionals. Lecture Notes in Statistics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5604-5_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5604-5_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90899-1
Online ISBN: 978-1-4612-5604-5
eBook Packages: Springer Book Archive