On the statistical power of Baarda’s outlier test and some alternative

Abstract

Baarda’s outlier test is one of the best established theories in geodetic practice. The optimal test statistic of the local model test for a single outlier is known as the normalized residual. Also other model disturbances can be detected and identified with this test. It enjoys the property of being a uniformly most powerful invariant (UMPI) test, but is not a uniformly most powerful (UMP) test. In this contribution we will prove that in the class of test statistics following a common central or non-central χ2 distribution, Baarda’s solution is also uniformly most powerful, i.e. UMPχ2 for short. It turns out that UMPχ2 is identical to UMPI, such that this proof can be seen as another proof of the UMPI property of the test. We demonstrate by an example that by means of the Monte Carlo method it is even possible to construct test statistics, which are regionally more powerful than Baarda’s solution. They follow a so-called generalized χ2 distribution. Due to high computational costs we do not yet propose this as a ”new outlier detection method”, but only as a proof that it is in principle possible to outperform the statistical power of Baarda’s test.

Keywords

• generalized χ2 test
• monte carlo method
• outlier test
• uniformly most powerful test