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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Vydáno v:Journal of applied statistics Ročník 42; číslo 9; s. 2056 - 2072
Hlavní autoři: Ghosh, Abhik, Basu, Ayanendranath
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 02.09.2015
Taylor & Francis Ltd
Témata:
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
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Abstract 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.
AbstractList The density power divergence (DPD) measure, defined in terms of a single parameter alpha , 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.
The density power divergence (DPD) measure, defined in terms of a single parameter a, 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.
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.
Author Basu, Ayanendranath
Ghosh, Abhik
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  organization: Interdisciplinary Statistical Research Unit, Indian Statistical Institute
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10.1201/b10956
10.1198/004017001316975880
10.1214/aoms/1177703732
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10.1093/biomet/85.3.549
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Snippet 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 ]....
The density power divergence (DPD) measure, defined in terms of a single parameter a, has proved to be a popular tool in the area of robust estimation [1]....
The density power divergence (DPD) measure, defined in terms of a single parameter alpha , has proved to be a popular tool in the area of robust estimation...
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SubjectTerms 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
Title Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach
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