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

TL;DR

This paper presents a simple, efficient fixed-pivot selection algorithm, extending it to weighted percentiles and other statistical measures, with implementations in MATLAB, C, and R to improve practical statistical computations.

Contribution

Introduces a fixed-pivot selection algorithm that simplifies implementation and enhances efficiency, with extensions to weighted percentiles and multiple statistical applications, provided in a MATLAB toolbox.

Findings

Simplifies selection algorithms with fixed pivot approach.

Reduces convergence time in statistical applications.

Provides versatile implementations in MATLAB, C, and R.

Abstract

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.