Open Access
Translator Disclaimer
June, 1995 On Optimal B-Robust Influence Functions in Semiparametric Models
Larry Z. Shen
Ann. Statist. 23(3): 968-989 (June, 1995). DOI: 10.1214/aos/1176324631


Bounded influence functions are used for robust estimation in semiparametric models. In this paper, we generalize Hampel's variational problem to semiparametric models and define the optimal B-robust influence function as the one solving the variational problem. We identify the lowest bounds for influence functions and establish the existence and uniqueness of the optimal influence functions in general semiparametric models. Explicit optimal influence functions are given for a special case. Examples are provided to illustrate the procedures for calculating the optimal influence functions and for constructing the corresponding optimal estimators.


Download Citation

Larry Z. Shen. "On Optimal B-Robust Influence Functions in Semiparametric Models." Ann. Statist. 23 (3) 968 - 989, June, 1995.


Published: June, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0844.62036
MathSciNet: MR1345209
Digital Object Identifier: 10.1214/aos/1176324631

Primary: 62F35
Secondary: 62G35

Keywords: B-robust , Hampel's problem , most robust estimate , optimal bounded influence function , semiparametric models

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 3 • June, 1995
Back to Top