Improved Score Tests in Symmetric Linear Regression Models |
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Authors: | Miguel A. Uribe-Opazo Gauss M. Cordeiro |
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Affiliation: | 1. Departamento de Matemática e Estatística , Universidade Estadual do Oeste do Paraná , Cascavel/PR, Brazil;2. Departamento de Física e Matemática , Universidade Federal Rural de Pernambuco , Recife/PE, Brazil |
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Abstract: | The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n ?3/2), n being the sample size. The corrections represent an improvement over the corresponding original Rao's score statistics, which are chi-squared distributed up to errors of order O(n ?1). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size. |
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Keywords: | Asymptotic distribution Bartlett-type correction Chi-squared distribution Score test Symmetric distribution t distribution |
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