Least Squares Adjustment and Accuracy Estimation in Multiplicative Error Models

To probe into the parameter estimation in multiplicative error models, three least squares (LS) adjustment methods, i.e., the LS method, the weighted LS method and the bias-corrected weighted LS method, in multiplicative error models were discussed based on the existing researches and using the least squares theory. Their accuracy estimation expressions were derived, the parameter estimations and the variance-covariance matrices were obtained, and the variances of unit weight were constructed for the three LS adjustment methods. A simulated example demonstrates that the bias-corrected weighted LS method is optimal and unbiased because in the example the estimations of unit weight variance are respectively 1.964 8, 0.999 8 and 0.980 7 to the LS method, the weighted LS method and the bias-corrected weighted LS method.