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digital STATISTICA & APPLICAZIONI - 2007 - 1
Digital issue
issue 1 - 2007
publisher Vita e Pensiero
format Digital issue | Pdf
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Inequality curve and inequality index based on the ratios between lower and upper arithmetic means
by Michele Zenga pages: 26 Download
A new inequaliy curve I(p) based on the ratio between the lower mean M(p) and the upper mean þ M+(p) is proposed. By averaging I(p) the new inequality index I is obtained. The index I satisfies the usual properties required to an inequality measure. Being U(p)=1-I(p) a ratio between two arithmetic means, the meaning of I(p) is very straightforward. The index I is related to the Gini index R and the Bonferroni index B by the relation: R <= B <= I . In section 6 the curves I(p) and the Lorenz curve L(p) for the N = 14026 personal incomes, regarding the Bank of Italy survey on the household expenditure, are reported.
Multidimensional poverty decomposition: a fuzzy set approach
by Stéphane Mussard, María Noel Pi Alperin pages: 24 Download
This article extends the paper of Dagum C. and Costa M. (2004). We further develop the study of multidimensional poverty using fuzzy sets by introducing a mixture of decomposition analysis. The model yields the most relevant dimensions of poverty (health, education, etc.) and the most relevant sub-groups (areas, gender, etc.) in order to identify the main forces that contribute to the overall amount of the state of poverty. These results are useful for decision makers that contemplate socioeconomic policies in favour of poverty reduction. Finally, we apply this decomposition to study the level of poverty of Argentina in 1998.
Models for categorical data: a comparison between the Rasch model and Nonlinear Principal Component Analysis
by Eugenio Brentari, Silvia Golia, Marica Manisera pages: 26 Download
The paper compares two models to construct measures from the responses on a set of categorical variables, the Rasch Model and the Nonlinear (Categorical) Principal Component Analysis, and can be considered as a part of the literature about the choice between stochastic and algorithmic models. The aim is to discuss the Rasch Model and Nonlinear PCA differences and similarities, emphasizing the information that can be drawn from the data, and to compare the resulting measures.
The educational and working experience household human capital in a structural model with formative and reflective indicators
by Pietro Giorgio Lovaglio pages: 24 Download
The aim of the present paper is to generalize the definition of Human Capital (HC) as unidimensional latent variable (LV) to the case of bidimensional LV composed by an ‘‘Educational dimension’’ and a ‘‘Working experience dimension’’ underlying the process of determination and accumulation of earned Income and capital Income. In particular we propose an extended version of the statistical definition of HC (part 2), coherent with the economic theory and major studies that have proposed HC indicators (part 3); then, in order to overcome the limits of classical approaches, an estimation method that provides standardized LV (part 4) and an actuarial approach that obtains HC scores in monetary values are proposed (part 6) and applied to the estimation of the Italian household HC in 2000 (part 5). Then, to investigate relations between HC and other relevant economic variables for household, a structural model is specified and estimated (part 7). Final section draws major conclusions (part 8).
Minimum sample sizes for confidence intervals for Gini’s mean difference: a new approach for their determination
by Francesca Greselin, Walter Maffenini pages: 20 Download
The sample mean difference  is an unbiased estimator of Gini’s mean difference A. It is well known that  is asymptotically normally distributed (Hoeffding, 1948). In order to obtain confidence intervals for A,  must be standardized and hence its variance Var(Â) must be estimated. In this paper we study the effective coverage of the confidence intervals for A, when using a specific unbiased estimator ^ Var(Â) for the variance of Â, in a non-parametric framework. The empirical determination of the minimum sample size required to reach a good approximation of the nominal coverage is analyzed through a new approach. The reported results show that this threshold is critically related to the asymmetry and the tail heaviness in the underlying distribution.