Exhaustive search procedure for multiple outlier detection

In the last decades many statistical tests based on the least squares solution have been proposed for multiple outlier detection. All of them suffer, however, from deficiencies that make them inefficient in their practical application. As recently demonstrated by the author, this situation is unavoidable in the framework of least squares theory. The present contribution elaborates on this impossibility of obtaining an unambiguous response for any statistical test based on the least squares solution and makes use of multiple least squares adjustments for statistically characterizing the equivalent sets of multiple gross error vectors. Several examples and a flexible Matlab implementation are provided.