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digital STATISTICA & APPLICAZIONI - 2014 - 1
Digital issue
issue 1 - 2014
publisher Vita e Pensiero
format Digital issue | Pdf
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Primo fascicolo del 2014


by Eugenio Brentari pages: 1 Download
The ordinal inter-rater agreement in the evaluation of university courses
by Donata Marasini, Piero Quatto, Enrico Ripamonti pages: 12 Download
In this paper we consider the problem of the evaluation of undergraduate and graduate courses, in the context of Italian universities. We present a descriptive measure of ordinal inter-rater agreement that can be associated with a suitable index of satisfaction. This measure is a modification of a previously proposed index, which avoids the problem of paradoxes of both Cohen’s and Fleiss’ kappa statistics. We apply our results to the evaluation of the Bachelors and Masters of Sciences in Economics at the University of Milan-Bicocca.
Zenga distribution: parameters estimation with constraints on synthetic inequality indices
by Alberto Arcagni pages: 22 Download
In 2010, Zenga introduced a three-parameter model for distributions by size, with Paretian right-tail and expectation always finite. This paper examines how to estimate its parameters with constraints on the expectation and on synthetic inequality indices, which are major characteristics to describe income distributions. These methods bring out new lights in the interpretation of the parameters.
Two methods for composite indicator dimension reduction based on rank correlation
by Marco Marozzi, Paolo Cozzucoli pages: 8 Download
Composite indicators are very useful in addressing complex variables that cannot be directly observed: they can be used to assess for example quality of life and customer satisfaction. In practice, it is very often of interest to reduce the dimension of a composite indicator by selecting among its components the most important ones. In this paper we propose a method for reducing the dimension of composite indicators based on the comparison of rank correlation coefficients and we compare it with another method. A practical application to university student satisfaction data is presented. Moreover, we evaluate how the choice of the rank correlation coefficient influences the results of the practical application.
Median estimation knowing the median of an auxiliary variable
by Rosita De Paola pages: 16 Download
This paper deals the estimation of a finite population median in the presence of an auxiliary variable. Two methods based on the regression estimator are studied along with the ratio estimator and the median’s estimator without auxiliary variable. These estimators are applicable in situations where only the population median of the auxiliary variable is known. On basis of all possible samples derived by symmetric and asymmetric (positive and negative) cases, the efficiency of these estimators are compared. It is shown that the estimators based on the regression estimator improve always the median’s estimation with regard to the estimator without the auxiliary variable, but for choosing the best estimator for the median it has been considered the combination of symmetric, positive asymmetric and negative asymmetric cases between the auxiliary variable (X) and the principal variable (Y).
The potential of the I(p) inequality curve in the analysis of empirical distributions
by Walter Maffenini, Marcella Polisicchio pages: 23 Download
The possibility of analysing the inequality of a frequency distribution through a point measure is undoubtedly an advantage for any socioeconomic research. The Lorenz curve is the cornerstone on which other global inequality measures have been subsequently introduced. Nonetheless, other point inequality measures have been put forward and have, in fact, revived the debate about it. The I(p) inequality measure stands out from these others because of its straightforward interpretation, its ease of computing and its non-predetermined behaviour. Throughout the present study, other positive aspects of the I(p) measure have been pointed out. In particular, we have highlighted its readiness to respond to translation and equalitarian transfers, and we have compared the I(p) curve with the Lorenz curve which does not show a similar response. In order to explain the descriptive and interpretative capacity of I(p), some real cases of Italian income distribution have been analysed. It is very interesting to note how easily the I(p) inequality point measure can graphically show the inequality among different groups of population, and how it can express the effect of the transformations that may occur in income distribution.
Some advances in Markov chain bootstrapping of continuous-valued stochastic processes
by Paolo Falbo, Cristian Pelizzari pages: 28 Download
Econometric analysis is continuously challenged by the new requirements emerging in different fields of research. Referring in particular to the area of finance and economics, numerical methods based on simulations are attempting to solve a wide range of problems (e.g. real and financial investment diversification, production optimization, pricing, hedging, etc.) of increasing complexity. A substantial help to these needs is coming from Markov chain bootstrapping, which is proving to be a powerful method to attack difficult simulation problems, where in particular the properties of a stochastic process can not be assessed clearly and trajectories show nonlinear dependences. In this paper, we expose some late advances in the research on Markov chain bootstrapping. In particular, we focus on the problem of adapting Markov chain theory (which is notoriously discrete-valued) to simulate continuous-valued stochastic processes in the sectors of electricity and environmental markets. As it is well known, the main processes governing these markets (i.e. prices and demand) can not be satisfactorily represented as geometric Brownian motions, as it is common for traditional financial markets. Indeed, nonlinearities are often recognized in the literature: spikes, stochastic volatility, seasonality, and switching regimes are typical features described in most econometric papers focusing on these markets. We apply our Markov chain bootstrapping and test its properties based on the time series of daily electricity prices observed on the German market.