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Robust Regression Estimation in Generalized Linear Models

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International Encyclopedia of Statistical Science

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The idea of generalized linear models (GLM) generated by Nelder and Wedderburn (1972) seeks to extend the domain of applicability of the linear model by relaxing the normality assumption. In particular, GLM can be used to model the relationship between the explanatory variable, X, and a function of the mean, μ i , of a continuous or discrete responses. More precisely, GLM assumes that g(μ i ) = η i =\({\sum\limits}_{j=1}^p x_ij \beta_j,\) where β = (β 1, β 2, …, β p )T is the p-vector of unknown parameters and g( ⋅) is the link function that determines the scale on which linearity is assumed. Models of this type include logistic and probit regression, Poisson regression, linear regression with known variance, and certain models for lifetime data.

Specifically, let Y 1, Y 2, …, Y n , be n independent random variables drawn from the exponential family with density (or probability function)

$$f({y}_{i};{\theta }_{i},\phi ) =\exp \left \{\frac{{y}_{i}{\theta }_{i} - b({\theta }_{i})}...

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Author information

Authors and Affiliations

  1. University of Malaya, Kuala Lumpur, Malaysia

    Aishah Hamzah (Professor)

  2. University of Rajshahi, Rajshahi, Bangladesh

    Mohammed Nasser (Professor)

Authors
  1. Aishah Hamzah
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  2. Mohammed Nasser
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Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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Hamzah, A., Nasser, M. (2011). Robust Regression Estimation in Generalized Linear Models. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_495

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