A drawback of robust statistical techniques is the increased computational effort often needed compared to non robust methods. Robust estimators possessing the exact fit property, for example, are NP-hard to compute. This means thatunder the widely believed assumption that the computational complexity classes NP and P are not equalthere is no hope to compute exact solutions for large high dimensional data sets. To tackle this problem, search heuristics are used to compute NP-hard estimators in high dimensions. Here, an evolutionary algorithm that is applicable to different robust estimators is presented. Further, variants of this evolutionary algorithm for selected estimatorsmost prominently least trimmed squares and least median of squaresare introduced and shown to outperform existing popular search heuristics in difficult data situations. The results increase the applicability of robust methods and underline the usefulness of evolutionary computation for computational statistics.
Evolutionary algorithms robust regression least trimmed squares (LTS) least median of squares (LMS) least quantile of squares (LQS) least quartile difference (LQD)