A Robust Rescaled Moment Test for Normality in Regression | Science Publications

Journal of Mathematics and Statistics

Habshah Midi¹  Md. S. Rana¹  A. H.M.R. Imon¹ 

关键词: Regression residuals;    outlier;    rescaled moments;    skewness;    kurtosis;    jarque-bera test;    robust rescaled moment test;   

DOI  :  10.3844/jmssp.2009.54.62

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evident that normality tests on residuals suffer from superimposed normality and often possess very poor power. Approach: This study showed that normality tests suffer huge set back in the presence of outliers. We proposed a new robust omnibus test based on rescaled moments and coefficients of skewness and kurtosis of residuals that we call robust rescaled moment test. Results: Numerical examples and Monte Carlo simulations showed that this proposed test performs better than the existing tests for normality in the presence of outliers. Conclusion/Recommendation: We recommend using our proposed omnibus test instead of the existing tests for checking the normality of the regression residuals.

【 授权许可】

Unknown