Abstract: Based on the mean shift outlier model,outliers are considered as the mean shift parameters of the corresponding observations,which can be estimated by using the least squares method.In literature,the estimation of the mean shift parameters is often formulated as the complicated linear function of the least squares residuals biased by the presence of outliers,and its statistical performance is not lucid.In this paper,the estimated mean shift parameters have been further derived and represented as a concise formula in the general case of correlated observations,from which the estimated mean shift parameters are interpreted with the concept of statistical prediction.Finally,the essential distinction between the estimated mean shift parameters and residuals is demonstrated by a practical example.