On the efficiency of Gini’s mean difference

Gerstenberger, Carina; Vogel, Daniel

doi:10.1007/s10260-015-0315-x

Cited by 43 publications

(28 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar expression has been later advanced for a generalized diversity measure [25,26]. Recently, the efficiency of the Gini mean difference has been shown in case of contaminated distributions [10].…”

Section: Heterogeneity: Concept and Measuresmentioning

confidence: 82%

Gini heterogeneity index for detecting uncertainty in ordinal data surveys

Capecchi

Iannario

2016

METRON

View full text Add to dashboard Cite

In sample surveys where people are asked to give responses to items by means of ordinal scales it is common to register an inherent indecision generated by both objective and subjective causes. Thus, an effective statistical analysis should take this component into account to avoid bias in estimation, interpretation and prediction. In this paper, we show that the heterogeneity index proposed by Gini and its variants are effective measures to detect such an uncertainty. The relationships of Gini heterogeneity index with the parameter of a mixture model are discussed and exploited as a tool for the exploratory selection of covariates. Then, a real case study is considered to check for the effectiveness of these proposals. Some concluding remarks end the paper.

show abstract

Section: Heterogeneity: Concept and Measuresmentioning

confidence: 82%

Gini heterogeneity index for detecting uncertainty in ordinal data surveys

Capecchi

Iannario

2016

METRON

View full text Add to dashboard Cite

show abstract

“…Similar to variance, GMD is another popular and superior measure of variability (Yitzhaki, ). Compared to variance, GMD is more robust (less susceptible to outliers and more efficient for heavy‐tailed distributions) (Gerstenberger & Vogel, ; Xiao & Lu, ). The GMD of a random variable X can be defined as:

G false(X false) = E |X - X^{'}|,

…”

Section: One‐way Distance Components Decomposition and Main Effect Sementioning

confidence: 99%

Multivariate Global Sensitivity Analysis Based on Distance Components Decomposition

2018

View full text Add to dashboard Cite

In this article, a new set of multivariate global sensitivity indices based on distance components decomposition is proposed. The proposed sensitivity indices can be considered as an extension of the traditional variance-based sensitivity indices and the covariance decomposition-based sensitivity indices, and they have similar forms. The advantage of the proposed sensitivity indices is that they can measure the effects of an input variable on the whole probability distribution of multivariate model output when the power of distance 0<α<2. When α=2, the proposed sensitivity indices are equivalent to the covariance decomposition-based sensitivity indices. To calculate the proposed sensitivity indices, an efficient Monte Carlo method is proposed, which can also be used to calculate the covariance decomposition-based sensitivity indices at the same time. The examples show the reasonability of the proposed sensitivity indices and the stability of the proposed Monte Carlo method.

show abstract

“…π{2 for the normal distributions, and a " 1 for the exponential distributions. See also Tables 2-3 in [17], for some other distributions. Therefore, assuming the existence of a superpopulation, we use the same constants for the estimation in the finite population.…”

Section: Model Of Outliersmentioning

confidence: 99%

“…The statistics MAD and IQR are efficient where data contain large outliers or/and the proportion of outliers is large, but they are relatively inefficient in the opposite case. Recently, it has been demonstrated by Gerstenberger and Vogel [17] that the GMD statistic combines advantages of the sample variance and the absolute mean deviation in the i.i.d. case.…”

Section: Introductionmentioning

confidence: 99%

Gini’s mean difference and variance as measures of finite populations scales

Čiginas

Pumputis

2015

Lith Math J

View full text Add to dashboard Cite

We consider Gini's mean difference statistic as an alternative to the empirical variance in the settings of finite populations, where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite-population context) estimation strategies for a scale of the population, related to the alternative statistic in a possible presence of outliers in the data.The paper also presents a wide comparative survey of properties of Gini's mean difference statistic and the empirical variance. It includes asymptotic properties of both statistics: the asymptotic normality, one-term Edgeworth expansions, and bootstrap approximations for Studentized versions of the statistics. Estimation of the variances and other parameters of the statistics is also studied, where we use auxiliary information available on the population elements. Theoretical results are illustrated by a simulation study. MSC: 62E20

show abstract

On the efficiency of Gini’s mean difference

Cited by 43 publications

References 13 publications

Gini heterogeneity index for detecting uncertainty in ordinal data surveys

Gini heterogeneity index for detecting uncertainty in ordinal data surveys

Multivariate Global Sensitivity Analysis Based on Distance Components Decomposition

Gini’s mean difference and variance as measures of finite populations scales

Contact Info

Product

Resources

About