Mean Shift versus Variance Inflation Approach for Outlier Detection—A Comparative Study

Abstract

Outlier detection is one of the most important tasks in the analysis of measured quantities to ensure reliable results. In recent years, a variety of multi-sensor platforms has become available, which allow autonomous and continuous acquisition of large quantities of heterogeneous observations. Because the probability that such data sets contain outliers increases with the quantity of measured values, powerful methods are required to identify contaminated observations. In geodesy, the mean shift model (MS) is one of the most commonly used approaches for outlier detection. In addition to the MS model, there is an alternative approach with the model of variance inflation (VI). In this investigation the VI approach is derived in detail, truly maximizing the likelihood functions and examined for outlier detection of one or multiple outliers. In general, the variance inflation approach is non-linear, even if the null model is linear. Thus, an analytical solution does usually not exist, except in the case of repeated measurements. The test statistic is derived from the likelihood ratio (LR) of the models. The VI approach is compared with the MS model in terms of statistical power, identifiability of actual outliers, and numerical effort. The main purpose of this paper is to examine the performance of both approaches in order to derive recommendations for the practical application of outlier detection.

Keywords

• mean shift model
• variance inflation model
• outlierdetection
• likelihood ratio test
• Monte Carlo integration
• data snooping