Robust estimation in generalized linear models: the density power divergence approach

The generalized linear model is a very important tool for analyzing real data in several application domains where the relationship between the response and explanatory variables may not be linear or the distributions may not be normal in all the cases. Quite often such real data contain a significa...

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Vydané v:Test (Madrid, Spain) Ročník 25; číslo 2; s. 269 - 290
Hlavní autori: Ghosh, Abhik, Basu, Ayanendranath
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2016
Springer Nature B.V
Predmet:
Cases (containers)
Counting
Data analysis
Density
Economics
Estimators
Finance
Generalized linear models
Insurance
Logistics
Management
Mathematical models
Mathematics and Statistics
Original Paper
Poisson distribution
Regression
Regression analysis
Statistical Theory and Methods
Statistics
Statistics for Business
Studies
United States > US
Logistic regression
Generalized linear model
Density power divergence
Robustness
62F35
Poisson regression
62J12
ISSN:1133-0686, 1863-8260
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Abstract The generalized linear model is a very important tool for analyzing real data in several application domains where the relationship between the response and explanatory variables may not be linear or the distributions may not be normal in all the cases. Quite often such real data contain a significant number of outliers in relation to the standard parametric model used in the analysis; in such cases inference based on the maximum likelihood estimator could be unreliable. In this paper, we develop a robust estimation procedure for the generalized linear models that can generate robust estimators with little loss in efficiency. We will also explore two particular special cases in detail—Poisson regression for count data and logistic regression for binary data. We will also illustrate the performance of the proposed estimators through some real-life examples.
AbstractList The generalized linear model is a very important tool for analyzing real data in several application domains where the relationship between the response and explanatory variables may not be linear or the distributions may not be normal in all the cases. Quite often such real data contain a significant number of outliers in relation to the standard parametric model used in the analysis; in such cases inference based on the maximum likelihood estimator could be unreliable. In this paper, we develop a robust estimation procedure for the generalized linear models that can generate robust estimators with little loss in efficiency. We will also explore two particular special cases in detail—Poisson regression for count data and logistic regression for binary data. We will also illustrate the performance of the proposed estimators through some real-life examples.
Author Basu, Ayanendranath
Ghosh, Abhik
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  surname: Basu
  fullname: Basu, Ayanendranath
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  organization: Interdisciplinary Statistical Research Unit, Indian Statistical Institute
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Keywords Logistic regression
Generalized linear model
Density power divergence
Robustness
62F35
Poisson regression
62J12
Language English
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SubjectTerms Cases (containers)
Counting
Data analysis
Density
Economics
Estimators
Finance
Generalized linear models
Insurance
Logistics
Management
Mathematical models
Mathematics and Statistics
Original Paper
Poisson distribution
Regression
Regression analysis
Statistical Theory and Methods
Statistics
Statistics for Business
Studies
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