Secondo fascicolo del 2005
by Aride Mazzali
Con questo numero la rivista Statistica & Applicazioni conclude il primo triennio di vita. L’esperienza acquisita, i nuovi orientamenti della ricerca scientifica ed i criteri di valutazione della stessa, ci stimolano ad apportare alcuni cambiamenti significativi già nel prossimo numero.
On the Decomposition of the Gini’s
Mean Difference and Concentration Ratio
by Michele Zenga, Paolo Radaelli
In this paper we propose a decomposition for the Gini’s mean difference of a real variate obtained as the sum of c variates observed on a finite population. The decomposition is mainly based on two different sortings of the values of each variate: one is the natural sorting of the values, the other one is obtained by ranking the values according to the corresponding totals. The obtained result is then applied to get a similar decomposition for the Gini’s concentration ratio. This latter decomposition is then compared with other decompositions proposed in literature. Finally the decompositions for the Gini’s mean difference and concentration ratio are extended to the more general case of a linear combination of variates.
Keywords: mean difference, concentration ratio, decomposition, uniform ranking.
On the completeness of the family
of factorizable densities
by Fulvia Mecatti, Carla Cattaneo
The family of continuous distribution laws which factorize in two positive functions, one depending on the variable only and the other one depending on a scalar parameter exclusively, is concerned. The family has no intersection with the Exponential class and includes Uniform distributions over an interval depending upon the parameter as well as infinitely many other distributions arising, for instance, by truncation. Simple sufficient conditions, regarding the support of random variables with distribution included in the family of factorizable densities and suitable to prove completeness are stated. Completeness of statistics based on sample from densities included in the family is also considered.
Keywords: Acceptance-Rejection method, Complete statistics, Non-regular distributions families, Truncated data.
Continuous Time Models to Extract a Signal in Presence of Irregular Surveys
by Edoardo Otranto, Roberto Iannaccone
A typical statistical problem arises when a time series consists of observations collected using two different timing intervals. This is often the case in Statistical Offices, when the frequency of their surveys changes. In such cases the classical tools to deal with signal extraction, such as the Hodrick-Prescott filter, are used on the most recent homogeneous span, losing information deriving from the previous period; alternative solutions are to aggregate or disaggregate the series to obtain the same frequency. To use all the available information we exploit the fact that the Hodrick-Prescott filter has a state-space representation in a continuous time support, which provides the possibility to deal with different spans. In this paper we investigate the advantages of the continuous time models in extracting a trend from a time series with respect to the Hodrick-Prescott filter in the presence of irregular surveys. The flexibility of this model will be highlighted through examples of Monte Carlo experiments and an application on real data.
Keywords: Hodrick-Prescott filter, smoothing parameter, cubic spline, state-space model.
A new index to measure association between cat-egorical and ordinal variables
by Angelo M. Mineo, Mariantonietta Ruggieri
In this paper a new index to analyse the dependence between categorical variables is presented and is compared to other measures of association, mainly based on the X2 Pearson’s statistic. The new index is compared to well-known measures of cograduation, as well. To restrict our comparisons, the domain we con-sider includes all the square contingency tables belonging to the same Fréchet class, that is all the contingency tables in which the marginal frequencies are given as fixed in both characters. Anyway, the new index is good even if there are no con-strain on the marginal distributions, but only a constrain on n, the total of the ob-servations.
Keywords: Fréchet class, association, cograduation, contingencies.
Capitale sociale e processi produttivi locali: un’analisi a livello provinciale
by Isabella Santini
Several empirical studies have shown the relevance of social capital to economic growth; nevertheless, some questions still need an answer: i) how strong is the impact of social capital on the production process? ii) what kind of relationship links social capital to traditional input factors, such as labour and physical capital? This paper attempts to answer to these questions at a macroeconomic level. Specifically, the paper aims to evaluate the role of social capital in the production process, the kind of relationship which links social capital to traditional input factors and the intensity of social capital impact on the production process. A case study referred to the Italian provinces will be presented.
Keywords: social capital, production process, production function, Cobb-Douglas.