An extended w-test for outlier diagnostics in linear models

Abstract

The issue of outliers has been a research focus in the field of geodesy. Based on a statistical testing method known as the w-test, data snooping along with its iterative form, iterative data snooping (IDS), is commonly used to diagnose outliers in linear models. However, in the case of multiple outliers, it may suffer from the masking and swamping effects, thereby limiting the detection and identification capabilities. This contribution is to investigate the cause of masking and swamping effects and propose a new method to mitigate these phenomena. First, based on the data division, an extended form of the w-test with its reliability measure is presented, and a theoretical reinterpretation of data snooping and IDS is provided. Then, to alleviate the effects of masking and swamping, a new outlier diagnostic method and its iterative form are proposed, namely data refining and iterative data refining (IDR). In general, if the total observations are initially divided into an inlying set and an outlying set, data snooping can be considered a process of selecting outliers from the inlying set to the outlying set. Conversely, data refining is then a reverse process to transfer inliers from the outlying set to the inlying one. Both theoretical analysis and practical examples show that IDR would keep stronger robustness than IDS due to the alleviation of masking and swamping effect, although it may pose a higher risk of precision loss when dealing with insufficient data.