GENERALISED LEAST SQUARE RATIO ESTIMATOR IN HETEROSCEDASTIC REGRESSION MODEL

In the presence of heteroscedastic errors, ordinary least square (OLS) estimators are not efficient and the usual test procedures lead to the improper conclusion. It may also lead to a wider confidence interval which increases the risk of Type-II error. In this situation, the generalised least squares estimator (GLSE) can be used which is not only unbiased but also efficient. In this paper, generalised least square ratio estimator (GLSRE) is proposed and showed that GLSRE is the same as least square ratio estimator (LSRE) under heteroscedasticity. Therefore, a simulation study is carried out to compare the performance of the generalised least square (GLS) estimator with the OLS estimator (OLSE) and the LSR estimator (LSRE) under heteroscedasticity by using total mean squared error (TMSE), mean absolute percentage error (MAPE) and false acceptance rate (FAR) as performance comparison measures. The simulation results show that LSRE outperforms the OLSE and GLSE in case of moderate to severe heteroscedasticity for all sample sizes and in case of weak to mild heteroscedasticity for relatively small samples. GLSE performs better than OLSE and LSRE irrespective of sample size as well as the level of heteroscedasticity in case of the small value of error variance and also in case of weak to mild heteroscedasticity for large samples. Performances of these methods are also compared based on a real-life application.