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Provides an applications-oriented introduction to robust regression and outlier detection, emphasising °high-breakdown° methods which can cope with a sizeable fraction of contamination. Its self-contained treatment allows readers to skip the mathematical material which is concentrated in a few sections. Exposition focuses on the least median of squares technique, which is intuitive and easy to use, and many real-data examples are given. Chapter coverage includes robust multiple regression, the special case of one-dimensional location, algorithms, outlier diagnostics, and robustness in related fields, such as the estimation of multivariate location and covariance matrices, and time series analysis.