Abstract:
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The averaged extreme regression quantile (AERQ) in the linear statistical model of dimension p and n observations is introduced in two possible ways: Either as a solution of a linear programming problém and/or as a one-step version, starting with a special rank estimator of the slopes and estimating the intercept separately. AERQ is a scalar statistic approaching the extreme of model errors. It is an extreme of all alpha-regression quantiles of the model for alpha between 0 and 1. Under a finite n, its deviation from the extreme model error is the smallest with respect to all possible ways of estimating the slope components of the linear model. The extreme R-estimator of the slopes even can estimate the slopes consistently for n increasing. As a solution of a linear programming problém, the AERQ is a convex combination of p among n regression responses, corresponding the optimal base.
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