Wild Bootstrap Uncertainty for Outlier Detection Using MM-Estimation in Concrete Compressive Strength Data

Abstract

Outlier detection in robust regression is typically expressed as a binary decision, even though the status of an observation can change upon repeated resampling. Using concrete compressive strength data, the study examines  uncertainty through a combination of MM-estimation and multiplier wild bootstrapping. The analysis begins with MM model estimation, and then a bootstrap pseudo-response is generated from leverage-adjusted residuals using multiplier weights. At each replication, the same robust procedure is reapplied to obtain the set of outliers and robust weights. Observation-level uncertainty is summarized by the probability of being an outlier, the probability of having a low weight, the mean of the bootstrap weights, and the standard deviation of the bootstrap weights. The results show that the Mammen, SUWB, and STPB schemes produce overlapping, but not identical, sets of problematic observations. Mammen provides the clearest separation between major outlier candidates and relatively stable observations. SUWB forms a denser core group, while STPB produces a more compressed outlier probability. In general, outlier status is better understood as a measure of stability rather than a fixed label. The approach provides a more informative basis for robust diagnostics and data quality assessment in concrete compressive strength modeling.