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Many statistical problems and applications require repeated computation oforder statistics, such as the median, but most statistical and programmingenvironments do not offer in their main distribution linear selectionalgorithms. We introduce one, formally equivalent to quickselect, which keepsthe position of the pivot fixed. This makes the implementation simpler and muchpractical compared with the best known solutions. It also enables an "oracular"pivot position option that can reduce a lot the convergence time of certainstatistical applications. We have extended the algorithm to weightedpercentiles such as the weighted median, applicable to data associated withvarying precision measurements, image filtering, descriptive statistics likethe medcouple and for combining multiple predictors in boosting algorithms. Weprovide the new functions in MATLAB, C and R. We have packaged them in a broadMATLAB toolbox addressing robust statistical methods, many of which can be nowoptimised by means of efficient (weighted) selections.

A practically efficient fixed-pivot selection algorithm and its extensible MATLAB suite