Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach

The density power divergence (DPD) measure, defined in terms of a single parameter α, has proved to be a popular tool in the area of robust estimation [ 1 ]. Recently, Ghosh and Basu [ 5 ] rigorously established the asymptotic properties of the MDPDEs in case of independent non-homogeneous observati...

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Bibliographic Details
Published in:Journal of applied statistics Vol. 42; no. 9; pp. 2056 - 2072
Main Authors: Ghosh, Abhik, Basu, Ayanendranath
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.09.2015
Taylor & Francis Ltd
Subjects:
Asymptotic methods
Density
density power divergence
Divergence
linear regressionmodel
Mathematical models
non-homogeneous data
Optimization
Parameter estimation
Parameter optimization
Primary: 62F35
Regression
Regression analysis
Robustness
Secondary: 62J05
Studies
Tuning
tuning parameter
ISSN:0266-4763, 1360-0532
Online Access:Get full text
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Summary:The density power divergence (DPD) measure, defined in terms of a single parameter α, has proved to be a popular tool in the area of robust estimation [ 1 ]. Recently, Ghosh and Basu [ 5 ] rigorously established the asymptotic properties of the MDPDEs in case of independent non-homogeneous observations. In this paper, we present an extensive numerical study to describe the performance of the method in the case of linear regression, the most common setup under the case of non-homogeneous data. In addition, we extend the existing methods for the selection of the optimal robustness tuning parameter from the case of independent and identically distributed (i.i.d.) data to the case of non-homogeneous observations. Proper selection of the tuning parameter is critical to the appropriateness of the resulting analysis. The selection of the optimal robustness tuning parameter is explored in the context of the linear regression problem with an extensive numerical study involving real and simulated data.
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ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2015.1016901