Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators

We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing...

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Bibliographic Details
Published in:Statistical methods & applications Vol. 30; no. 3; pp. 973 - 1005
Main Authors: Basu, Ayanendranath, Ghosh, Abhik, Mandal, Abhijit, Martin, Nirian, Pardo, Leandro
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021
Springer Nature B.V
Subjects:
Asymptotic properties
Chemistry and Earth Sciences
Computer Science
Density
Economics
Finance
Generalized linear models
Health Sciences
Humanities
Inference
Insurance
Law
Management
Mathematics and Statistics
Medicine
Original Paper
Parameter estimation
Physics
Regression models
Robustness (mathematics)
Statistical models
Statistical Theory and Methods
Statistics
Statistics for Business
Statistics for Engineering
Statistics for Life Sciences
Statistics for Social Sciences
Wald-type tests
Minimum density power divergence estimator
Robustness
Generalized linear models
ISSN:1618-2510, 1613-981X
Online Access:Get full text
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Summary:We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing any general composite null hypothesis about the GLM. The asymptotic and robustness properties of the proposed tests are also examined for the GLM with random design. Application of the proposed robust inference procedures to the popular Poisson regression model for analyzing count data is discussed in detail both theoretically and numerically through simulation studies and real data examples.
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ISSN:1618-2510
1613-981X
DOI:10.1007/s10260-020-00544-4