STATISTICA & APPLICAZIONI - 2020 - 1 - autori-vari - Vita e Pensiero - Fascicolo digitale Statistica & Applicazioni

STATISTICA & APPLICAZIONI - 2020 - 1

digital STATISTICA & APPLICAZIONI - 2020 - 1
Digital issue
journal STATISTICA & APPLICAZIONI
issue 1 - 2020
title STATISTICA & APPLICAZIONI - 2020 - 1
publisher Vita e Pensiero
format Digital issue | Pdf
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Primo fascicolo del 2020

CONTENTS

Editorial
by Eugenio Brentari pages: 1 Download
Density-weighted quantile regression
by Ilaria Lucrezia Amerise, Agostino Tarsitano pages: 16 Download
Abstract
This study proposes a new weighted quantile regression method through the introduction of weights based on a recursive estimation of the density function of residuals. The new estimators are strictly related to the quantity quantile method introduced by Radaelli and Zenga in 2006. More specifically, density-weighted quantile regression is an attempt to extend the idea of quantity quantiles within the framework of an iteratively re-weighted quantile regression in which each iteration involves the interpolating of the first-moment density function of the dependent variable.Densityweighted estimators are applied in an econometric setting to demonstrate their utility for analyzing the size distribution of transferable variables.
Flexible bivariate generalized Pareto models
by Barry C. Arnold pages: 7 Download
Abstract
The hierarchy of Pareto models, described in a paper written by Arnold in 2015, admit representations in terms of independent gamma variables. Utilizing general bivariate beta(2) models introduced in a paper written by Arnold and Ng in 2011, which also involve independent gamma components, it is possible to identify flexible bivariate generalized Pareto models which can exhibit a wide range of correlation values. Multivariate extensions of the models are described. Simplified submodels of these are amenable to standard inference strategies.
Deprivation, satisfaction and dual expressions of Gini related measures of inequality, mobility and convergence
by Elena Bárcena Martín, Jacques Silber pages: 19 Download
Abstract
This paper starts by presenting simple ways of computing the Gini index. We emphasize the dual ways of defining the Gini index and the possibility of expressing this index in terms of deprivation and satisfaction. These additional interpretations are then extended to the measurement of distributional change and convergence.
A joint decomposition of the Zenga-84 inequality index
by Francesca De Battisti, Francesco Porro pages: 7 Download
Abstract
This paper provides a multi-decomposition (or joint decomposition) of the Zenga-84 inequality index, considering simultaneously different sources and subpopulations. The suggested procedure consists of two different stages: in the first one, each inequality pointwise measure is decomposed by sources and by subpopulations; in the second one, the decomposition of the synthetic index is obtained, by averaging the previously decomposed pointwise measures. An important feature of this multi-decomposition is that it allows to assess the portion of the global inequality related to each source in each subpopulation, since most of the decomposition procedures proposed in the literature are not able to achieve such goal. The proposed joint decomposition permits also to obtain, as particular cases, two ‘‘marginal’’ decompositions by sources and by subpopulations of the Zenga-84 index, already introduced in the literature. To show the usefulness of the described multi-decomposition, an application about the household consumption is provided. The real considered dataset comes from the Household Consumption Expenditure Survey provided by ISTAT.
The joint decomposition of the Pietra index
by Francesco Porro, Mariangela Zenga pages: 7 Download
Abstract
In this paper, a multi-decomposition of the Pietra index is presented. This innovative methodology allows to achieve a relevant task, since it combines simultaneously the two most celebrated kinds of decomposition: by sources and by subpopulations. The key result of the proposed procedure is the detail level of decomposition: it allows to split the value of the index, by assessing the contribution of each source in each subpopulation. It is worth noting that this final result is not reached by all the decomposition procedures, since most of them do not permit to identify the contributions at so detailed level. The proposed joint decomposition is a sort of generalization, since from it two decompositions by sources and by subpopulations of the Pietra index, already proposed in the literature, can be obtained. Beyond the methodological details, an application based on the Survey Household Income and Wealth 2018 – carried out by Bank of Italy – is provided in order to clarify the advantages of the procedure.
Decomposition by subpopulations of Gini, Bonferroni and Zenga inequality measures
by Igor Valli, Michele Zenga pages: 45 Download
Abstract
This paper presents a common framework for the decompositions by subpopulations of Gini, Bonferroni and Zenga synthetic inequality measures. These three synthetic indexes are the weighted arithmetic means of the corresponding point measures and applying the Zenga two-step approach, decompositions based on means comparison are obtained. In the first step additive decompositions are derived for the point indexes and in the second step, using the decompositions of the point measures, we obtain the decompositions by subpopulations of the synthetic indexes. In particular the point and the synthetic indexes are decomposed in the sum of subpopulations contributions which in turn are decomposed in within and between components. The decompositions obtained can be utilized in the case of non-overlapping subpopulations as well as in the overlapping case and in the present work two numerical examples are illustrated to pointing out that whereas it is possible to obtain negative contributions for the Gini and the Bonferroni indexes, this cannot happen for the Zenga index.

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