Comparing the Robustness of Statistical Estimators of Proficiency Testing Schemes for a Limited Number of Participants

Abstract

This study aims at developing models in analyzing the results of proficiency testing (PT) schemes for a limited number of participants. The models can determine the best estimators of location and dispersion using unsatisfactory results as a criterion by combining: (a) robust and classical estimators; (b) kernel density plots; (c) Z-factors; (d) Monte Carlo simulations; (e) distributions derived from the addition of one or two contaminating distributions and one main Gaussian. The standards ISO 13258:2015, ISO 5725:2:1994, and EN ISO/IEC 17043:2010 are the basis of the analysis. The study describes an algorithm solving the optimization problem for (a) Gaussian, bimodal or trimodal distributions; (b) participating labs from 10 to 30; (c) fraction of the contaminating population up to 0.10; (d) variation coefficient of the main distribution equal to 2; (e) equal standard deviations of all the distributions, and provide figures with the optimal estimators. We also developed a generalized algorithm using kernel density plots and the previous algorithm, which is not subject to restrictions (b)–(e) and implemented in the results of a PT for the 28-day strength of cement with 12–13 participants. Optimal estimators’ figures and the generalized algorithm are helpful for a PT expert in choosing robust estimators.

Fundamentally Good Alternative to Normal Distribution

“…The good (i.e., unbiased, efficient and consistent) estimators of location (location measures) such as the mean, median and mode are the same. These estimators, except for the median, are sensitive to outliers or contaminations and insufficient to describe a distribution because two random variables or distributions with different dispersion may have the same location estimates [13]; [14].…”

“…The good estimators of dispersion (dispersion measures) such as the variance or standard deviation and coefficient variation are very related and important parameters. These estimators are sensitive to outliers or contaminations and insufficient to describe distributions because they are either location-invariant or scale-invariant and lack scale-and-location invariant property [13]; [14]. The estimates of the relative estimator of dispersion (i.e., coefficient of variation) lacks a bounded range and approaches infinity as the mean of the distribution tends to zero.…”

“…In literatures, there have been decades-old of numerous characterization, evaluation and performance studies on dispersion estimators (from the efficient as well as the robust categories of good estimators) under normal and other distributions such as the studies by [3]; [4]; [5]; [6]; [7]; [8]; [9]; [10]; [11]; [12]; [13]; [14]. Despite that, little or no attention was given to the alternative parameterization of a normal distribution so that the additivity and scaling transformations on an independent and identically distributed random variable gives to a distribution good (i.e., fundamentally correct) with any location-invariant, scale-invariant, and scale-and-location-invariant estimator.…”

Automatic Sequential Stitching of High-Resolution Panorama for Android Devices Using Precapture Feature Detection and the Orientation Sensor

“…The authors in [ 8 ] introduced the Accelerated-KAZE (AKAZE) algorithm, which is also based on nonlinear distribution filters such as KAZE, but its nonlinear scale-spaces are built using an efficient computer framework called Fast Explicit Diffusion (FED). The AKAZE detector is based on the Hessian Matrix.…”

“…Therefore, the outlier rejection phase is mandatory for the accurate fitting of the transformation model. Some robust probabilistic models such as Random Sample Consensus (RANSAC) [ 10 ], Progressive Sample Consensus (PROSAC) [ 11 ], and M-estimator Sample Consensus (MSAC) [ 8 ] can be used for outlier rejection in matched features and for fitting the transformation model.…”