Advances and Applications in Statistics
Volume 5, Issue 1, Pages 51 - 86
(April 2005)
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PARAMETRIC ROBUST TESTS FOR MULTIPLE REGRESSION PARAMETERS UNDER GENERALIZED LINEAR MODELS
Tsung-Shan Tsou (Taiwan) and Li-Chu Chien (Taiwan)
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Abstract: Parametric robust approach is proposed for making inferences about any subset of regression parameters in the setting of generalized linear models for continuous random variables. The proposed method is asymptotically legitimate so long as the true underlying distributions have finite second moments. Applications of the novel robust method to the analysis of variance (ANOVA) problems are provided. The one-way ANOVA, one-way analysis of covariance (ANCOVA) and two-way ANOVA situations are scrutinized in details. In spite of the fact that both the ordinary normal regression and ordinary gamma regression models could be made robust, the adjusted robust gamma regression (RGR) model is demonstrated to be more efficient than the adjusted robust normal regression (RNR) model for the analysis of commonly encountered nonnegative continuous random variables. |
Keywords and phrases: robust profile likelihood, generalized linear models, ANOVA, robust gamma regression, robust normal regression. |
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