Electronic Journal of Statistics

Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression

Abhik Ghosh and Ayanendranath Basu

Full-text: Open access

Abstract

In real life we often have to deal with situations where the sampled observations are independent and share common parameters in their distribution but are not identically distributed. While the methods based on maximum likelihood provide canonical approaches for doing statistical inference in such contexts, it carries with it the usual baggage of lack of robustness to small deviations from the assumed conditions. In the present paper we develop a general estimation method for handling such situations based on a minimum distance approach which exploits the robustness properties of the density power divergence measure (Basu et al. 1998 [2]). We establish the asymptotic properties of the proposed estimators, and illustrate the benefits of our method in case of linear regression.

Article information

Source
Electron. J. Statist., Volume 7 (2013), 2420-2456.

Dates
First available in Project Euclid: 2 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1380719361

Digital Object Identifier
doi:10.1214/13-EJS847

Mathematical Reviews number (MathSciNet)
MR3117102

Zentralblatt MATH identifier
1349.62087

Subjects
Primary: 62F35: Robustness and adaptive procedures
Secondary: 62J05: Linear regression

Keywords
Density power divergence robustness linear regression

Citation

Ghosh, Abhik; Basu, Ayanendranath. Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression. Electron. J. Statist. 7 (2013), 2420--2456. doi:10.1214/13-EJS847. https://projecteuclid.org/euclid.ejs/1380719361


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References

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