Advances and Applications in Statistics
Volume 10, Issue 2, Pages 259 - 275
(December 2008)
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A SIMPLE NUMERICAL METHOD OF CHECKING NORMALITY IN STATISTICAL MODELS
Isao Shoji (Japan)
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Abstract: This paper provides a simple numerical method of checking the normality of estimators such as the least square estimator and the maximum likelihood estimator. Instead of conventional analysis in which the parameter of interest is fixed, we allow the parameter to move around some parameter space. For each parameter sampled randomly out of the space, we get the parameter estimate and construct the Wald type test statistic which is used for checking normality of the estimator. We carry out several numerical experiments in a linear regression model and time series models such as AR, ARCH, GARCH and EGARCH to see how estimators behave as sample sizes are increasing. The results imply that conditional heteroscedasticity models require relatively large sample for good approximation of the normality. |
Keywords and phrases: asymptotic
normality, numerical analysis, finite sample, c2 test,
regression model, conditional heteroscedasticity model. |
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