¿Debemos pensar en un estimator diferente para la mediana?
Should we think of a different median estimator?
Abstract (en)
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 (Harrell & Davis 1982) estimators of the median for eight 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.
Abstract (es)
La mediana, una de las medidas de tendencia central más populares y utilizadas en la práctica, es el valor numérico que separa los datos en dos partes iguales. A pesar de su popularidad y aplicaciones, muchos desconocen la existencia de diferentes expresiones para calcular este parámetro. A continuación se presentan los resultados de un estudio de simulación en el que se comparan el estimador clásico y el propuesto por Harrell & Davis (1982). Mostramos que, comparado con el estimador de Harrell–Davis, el estimador clásico no tiene un buen desempeño para tamaños de muestra pequeños. Basados en los resultados obtenidos, se sugiere promover la utilización de un mejor estimador para la mediana.
References
Bassett, J. G. W. (1991), ‘Equivariant, monotonic, 50 % breakdown estimators’, The American Statistician 45(2), 135–137.
Harrell, F. E. & Davis, C. E. (1982), ‘A new distribution-free quantile estimator’, Biometrika 69(3), 635–640.
R Core Team (2013), R: A Language and Environment for Statistical Computing,
R Foundation for Statistical Computing, Vienna, Austria.*http://www.R-project.org/
Yoshizawa, C. N. (1984), Some Symmetry Tests, Institute of Statistics, Mimeo Series No. 1460. University of North Carolina, Chapel Hill, USA.
Zielinski, R. (1995), ‘Estimating median and other quantiles in nonparametric models’, Applicationes Mathematicae 23(3), 363–370.
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