A New Outlier Detection Method Considering Outliers As Model Errors

Outlier detection is an important task for fitting a model to a set of data. Two different outlier detection approaches are given as tests for outliers and robust methods. For these approaches, usually outliers are considered as additive bias terms neglected in the original adjustment model. However, there is another approach that outlier is considered as a model error in the Gauss–Markov model. This model error is represented as an unknown parameter. As it cannot be known before which observation includes outlier; this method is applied on the data for each observation separately and tested with t-test or F-test. It is successful if the sample includes only one outlier. To detect multiple outliers more successfully, in this article, a new outlier detection method is introduced. In this method, all the possible combinations of multiple outliers are considered as model errors and it is accepted that the smallest variance of them gives the solution for a certain number of outliers, then the estimated model errors are detected by comparing with a critical value. The critical value is chosen as 3σo. To compare the results of the new method, with those of the Least Median of Squares (LMS) and Huber M-estimators, Monte Carlo simulation technique is used for linear regression. The Mean Success Rate is proposed to measure the reliabilities of the methods. We showed that the new method is robust and includes the property of high breakdown point as LMS; and more efficient than LMS.