In this study, the knowledge of parameter estimation theory based on the corrected score (CS) approach is extended in a linear multivariate multiple regression model with heteroscedastic measurement errors (HME) and an unknown HME variance. The heteroscedasticity of the HME variance is assumed to be capable of being grouped into similar patterns where the sample of observations are assembled into several sub-samples with the property that the variances of the measurement error (ME) are homoscedastic within a group but heteroscedastic between ...