Goodness of Fit Test Based on BLUS Residuals for Error Distribution of Regression Model

The error distribution testing plays an important role in linear regression as distribution misspecification seriously affects the validity and efficiency of regression analysis. The least squares (OLS) residuals are often used to construct test statistics; in order to overcome the non-independent and identically residuals, the best linear unbiased scale (BLUS) residuals are applied in this paper, which, unlike OLS residuals, the residuals vector is identically and independently distributed. Based on the BLUS residuals, a new test statistic is constructed by using the sample random distance between sample quantile and quasi sample quantile derived from the null distribution, and the goodness-of-fit test of error distribution in the linear model is studied. The powers of the new tests under certain alternatives are examined. They are more powerful tests for the hypotheses concerned.