一个实用的固定主元选择算法及其可扩展的MATLAB集
A practically efficient fixed-pivot selection algorithm and its extensible MATLAB suite
摘要：
许多统计问题和应用需要重复计算顺序统计量，例如中位数，但大多数统计和编程环境在其主要分布中不提供线性选择算法。我们介绍一个，形式上相当于快速选择，它保持固定的枢轴的位置。这使得实现更简单，更实用的最佳已知的解决方案相比。它还启用了一个“预言”枢轴位置选项，可以大大减少某些统计应用程序的收敛时间。我们已经将该算法扩展到加权中值，例如加权中值，适用于与不同精度测量、图像滤波、描述性统计（如medcouple）相关的数据，以及用于在增强算法中组合多个预测因子。在MATLAB、C语言和R语言中提供了新的函数。我们已经将它们打包在一个广泛的MATLAB工具箱中，解决了强大的统计方法，其中许多方法现在可以通过有效的（加权）选择进行优化。
英文摘要：
Many statistical problems and applications require repeated computation of order statistics, such as the median, but most statistical and programming environments do not offer in their main distribution linear selection algorithms. We introduce one, formally equivalent to quickselect, which keeps the position of the pivot fixed. This makes the implementation simpler and much practical compared with the best known solutions. It also enables an "oracular" pivot position option that can reduce a lot the convergence time of certain statistical applications. We have extended the algorithm to weighted percentiles such as the weighted median, applicable to data associated with varying precision measurements, image filtering, descriptive statistics like the medcouple and for combining multiple predictors in boosting algorithms. We provide the new functions in MATLAB, C and R. We have packaged them in a broad MATLAB toolbox addressing robust statistical methods, many of which can be now optimised by means of efficient (weighted) selections.
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