A robust approach for generalized linear models based on maximum Lq-likelihood procedure
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909281519927296 |
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| author | Osorio, Felipe Galea, Manuel Gimenez, Patricia |
| author_facet | Osorio, Felipe Galea, Manuel Gimenez, Patricia |
| contents | In this paper we propose a procedure for robust estimation in the context of generalized linear models based on the maximum Lq-likelihood method. Alongside this, an estimation algorithm that represents a natural extension of the usual iteratively weighted least squares method in generalized linear models is presented. It is through the discussion of the asymptotic distribution of the proposed estimator and a set of statistics for testing linear hypothesis that it is possible to define standardized residuals using the mean-shift outlier model. In addition, robust versions of deviance function and the Akaike information criterion are defined with the aim of providing tools for model selection. Finally, the performance of the proposed methodology is illustrated through a simulation study and analysis of a real dataset. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_04176 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A robust approach for generalized linear models based on maximum Lq-likelihood procedure Osorio, Felipe Galea, Manuel Gimenez, Patricia Methodology 62J12, 62F35 In this paper we propose a procedure for robust estimation in the context of generalized linear models based on the maximum Lq-likelihood method. Alongside this, an estimation algorithm that represents a natural extension of the usual iteratively weighted least squares method in generalized linear models is presented. It is through the discussion of the asymptotic distribution of the proposed estimator and a set of statistics for testing linear hypothesis that it is possible to define standardized residuals using the mean-shift outlier model. In addition, robust versions of deviance function and the Akaike information criterion are defined with the aim of providing tools for model selection. Finally, the performance of the proposed methodology is illustrated through a simulation study and analysis of a real dataset. |
| title | A robust approach for generalized linear models based on maximum Lq-likelihood procedure |
| topic | Methodology 62J12, 62F35 |
| url | https://arxiv.org/abs/2408.04176 |