Journal
JOURNAL OF GEODESY
Volume 86, Issue 12, Pages 1137-1146Publisher
SPRINGER
DOI: 10.1007/s00190-012-0569-0
Keywords
Outlier detection; Gauss-Markov model; Hypothesis testing
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We investigate extreme studentized and normalized residuals as test statistics for outlier detection in the Gauss-Markov model possibly not of full rank. We show how critical values (quantile values) of such test statistics are derived from the probability distribution of a single studentized or normalized residual by dividing the level of error probability by the number of residuals. This derivation neglects dependencies between the residuals. We suggest improving this by a procedure based on the Monte Carlo method for the numerical computation of such critical values up to arbitrary precision. Results for free leveling networks reveal significant differences to the values used so far. We also show how to compute those critical values for non-normal error distributions. The results prove that the critical values are very sensitive to the type of error distribution.
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