Wild Bootstrap Uncertainty for Outlier Detection Using MM-Estimation in Concrete Compressive Strength Data
DOI:
https://doi.org/10.17509/s6e65802Keywords:
Concrete compressive strength, MM-estimator, Observation-level diagnostics, Outlier uncertainty, Robust regression, Wild bootstrapAbstract
The concrete compressive strength data may be heteroscedastic, contain influential observations, and exhibit atypical test results, such that a single robust fit is not adequate for the stability assessment of outlier decisions. In this paper, we develop a wild bootstrap-based uncertainty framework for observation-level outlier diagnostics under MM-estimation. First, a baseline MM-regression is fitted to the concrete compressive strength dataset. We apply the HC2 leverage correction to the centred residuals and perturb these residuals with three wild bootstrap multipliers: Mammen, Scaled Uniform Wild Bootstrap, and Symmetric Three-Point Bootstrap. Each pseudo-response is refitted using the same MM-estimation technique, and the outlier labels and robust weights are summarised by outlier probability, low-weight probability, mean bootstrap weight, and standard deviation of bootstrap weight. The results reveal that the three approaches detect partially overlapping outlier candidates but differ in the intensity of separation. Mammen has the sharpest separation, while SUWB has a compact core-candidate group, and STPB has a more conservative structure. The proposed methodology translates binary outlier labels to traceable diagnostic uncertainty measurements.
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