Time-Efficient Algorithms for Robust Estimators of Location, Scale, Symmetry, and Tail heaviness

Abstract

The analysis of the empirical distribution of univariate data often includes the computation of location, scale, skewness, and tail-heaviness measures, which are estimates of specific parameters of the underlying population distribution. Several measures are available, but they differ by Gaussian efficiency, robustness regarding outliers, and meaning in the case of asymmetric distributions. In this article, we briefly compare, for each type of parameter (location, scale, skewness, and tail heaviness), the “classical” estimator based on (centered) moments of the empirical distribution, an estimator based on specific quantiles of the distribution, and an estimator based on pairwise comparisons of the observations. This last one always performs better than the other estimators, particularly in terms of robustness, but it requires a heavy computation time of an order of n

Reference

Wouter Gelade, Vincenzo Verardi, Catherine Vermandele “Time-Efficient Algorithms for Robust Estimators of Location, Scale, Symmetry, and Tail heaviness” (2015) DOI: 10.1177/1536867X1501500105

@Article{gelade2015,
  title = {Time-Efficient Algorithms for Robust Estimators of Location, Scale, Symmetry, and Tail heaviness},
  volume = {15},
  issn = {1536-867X, 1536-8734},
  url = {http://journals.sagepub.com/doi/10.1177/1536867X1501500105},
  doi = {10.1177/1536867X1501500105},
  abstract = {The analysis of the empirical distribution of univariate data often includes the computation of location, scale, skewness, and tail-heaviness measures, which are estimates of specific parameters of the underlying population distribution. Several measures are available, but they differ by Gaussian efficiency, robustness regarding outliers, and meaning in the case of asymmetric distributions. In this article, we briefly compare, for each type of parameter (location, scale, skewness, and tail heaviness), the “classical” estimator based on (centered) moments of the empirical distribution, an estimator based on specific quantiles of the distribution, and an estimator based on pairwise comparisons of the observations. This last one always performs better than the other estimators, particularly in terms of robustness, but it requires a heavy computation time of an order of n},
  language = {en},
  number = {1},
  urldate = {2022-08-02},
  journal = {The Stata Journal: Promoting communications on statistics and Stata},
  author = {Gelade, Wouter and Verardi, Vincenzo and Vermandele, Catherine},
  month = {apr},
  year = {2015},
  pages = {77--94}
}