The Annals of Statistics

On Optimal B-Robust Influence Functions in Semiparametric Models

Larry Z. Shen

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 23, Number 3 (1995), 968-989.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324631

Digital Object Identifier
doi:10.1214/aos/1176324631

Mathematical Reviews number (MathSciNet)
MR1345209

Zentralblatt MATH identifier
0844.62036

JSTOR
links.jstor.org

Subjects
Primary: 62F35: Robustness and adaptive procedures
Secondary: 62G35: Robustness

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

Citation

Shen, Larry Z. On Optimal B-Robust Influence Functions in Semiparametric Models. Ann. Statist. 23 (1995), no. 3, 968--989. doi:10.1214/aos/1176324631. https://projecteuclid.org/euclid.aos/1176324631


Export citation