An effective approach towards efficient estimation of general linear model in case of heteroscedastic errors

Aiming at minimizing the ratio of error with respect to the response variable, the least squares ratio is a relatively new method for estimating the regression parameters. In the current article, the performance of this new approach is compared with the traditional OLS approach in the case when homoscedasticity of errors assumption is violated. A comparison is made through a simulation study using mean square error, mean absolute percentage error, and false acceptance rate as performance measures. It is observed that the least square ratio method outperforms the OLS method in case of moderate or severe heteroscedasticity for all sample sizes and in case of weak or mild heteroscedasticity for relatively small samples. Generally, it is noted that the efficiency of the least squares ratio method increases with an increase in the severity of heteroscedasticity as well as an increase in values of common error variance. The use of the least squares ratio method is recommended in case of mild or moderate to severe heteroscedasticity. Similar results were obtained from two real-life examples.

Automated summary

This article compares the performance of the least squares ratio method with the traditional OLS method under heteroscedasticity conditions. Simulation study and real-life examples show that the least squares ratio method outperforms the OLS method in cases of moderate to severe heteroscedasticity and small sample sizes.