Should we think of a different Median estimator?

Abstract

The median, one of the most popular measures of central tendency widely-used in the statistical practice, is often described as the numerical value separating the higher half of the sample from the lower half. Despite its popularity and applications, many people are not aware of the existence of several formulas to estimate this parameter. We present the results of a simulation study comparing the classic and the Harrell & Davis (1982) estimators of the median for seven continuous statistical distributions. It is shown that, relatively to the latter, the classic estimator performs poorly when the sample size is small. Based on these results, we strongly believe that the use of a better estimator of the median must be promoted.

Automatic detection of discordant outliers via the Ueda’s method

“…To study the performance of the Ueda's method, a simulation study was carried out using a similar simulation scheme to that presented by Vélez and Correa (2014), and following the recommendations by Salazar and Baena (2009). In brief, n observations of a particular probability distribution (see Table 1) are generated and a measure of interest is calculated.…”

Performance of Some Estimators of Relative Variability

“…The methods studied here are by no means exhaustive; indeed, further variations could be conceived by using other estimators of location and scale. For example, it has been shown that the Harrell-Davis version of the median outperforms the classic median estimator [79,125], the 20% trimmed mean tends to work well in many practical situations [126], and estimators of the mode have been shown to be highly efficient [127]. As for estimators of scale, in addition to those already in use (i.e., the SD, MAD, MnAD and IQR), estimators such as the percentage bend midvariance, the biweight midvariance or the τ measure of variation could be used [44].…”

“…We shall say that the jth estimator was better than an alternative to the classic estimator of the CV if γ j < 1. In this sense, γ j can be seen as a measure of efficiency [79]. We can rescale γ to log 10 (γ ) which represents a measure's information or weight of evidence [80] given in ban or dig (short for decimal digit).…”

“…A similar experimental design to the Monte Carlo scheme was described by Vélez and Correa [79], Marmolejo-Ramos et al [84] and Vélez et al [85]. The number of simulation runs B is equal to 10,000.…”

Current Topics in Statistical Graphics

“…It is worth mentioning that these researchers borrowed visual concepts from physics, specifically centre of gravity and area, to represent the effects of replacing missing values on experimental conditions means and variances). Finally, Figure 1D exemplifies how statistical graphics are valuable in communicating the results of analyses: Comparison of the performance of two robust estimators of central tendency (γ) on a Gamma distribution (with combinations of different values in the parameters α and β) of sample size five (source: Figure 2 in Vélez & Correa, 2014). Given new developments in methods for the visualisation of quantitative and categorical data, it is important to become aware of the latest advances in order to probe potential cross-field implementations or further the capabilities of the graphical methods.…”