Traditional statistical procedures are widely used because they offer the user a unified methodology with which to attack a multitude of problems, from simple location problems to highly complex experimental designs. These procedures are based on least squares fitting, but can be easily impaired by outlying observations. Indeed one outlying observation is enough to spoil the least squares fit, its associated diagnostics and inference procedures. Even though traditional inference methods are exact when the errors in the model follow a Normal distribution, they can be quite inefficient when the distribution of the errors has longer tails than the Normal distribution. This book offers an alternative, based on ranks of the data, to the least squares approach. Topics include one- and two-sample location models, linear models (including multiple regression and designed experiments), and multivariate models. Rank tests and estimates for all models are developed, including bounded influence and high breakdown methods. Emphasis is on efficiency and robustness and all methods are illustrated on data sets.
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