Vita e Pensiero

SUMMARY Mobility indices are important tools for summarizing and comparing the dynamics of different samples. A mobility index is defined as a function which assigns a real value I to a given transition matrix . The function I ðPÞ, where P is the transition matrix, is chosen to describe a specific type of mobility (e.g. the tendency to leave the current state). In this paper we develop a family of mobility indices capable of embodying information on both the intensity and the prevailing direction of mobility in the sample under study. Keywords: Mobility Index, Transition Matrix, Prevailing Direction.

SUMMARY For several years it has become the practice of Public Administration quality assessment as part of the institutional activities carried out by offices to improve public services by monitoring the production process. The Ministry of Labour and Social Policies has adopted a system of ‘‘quality assessment’’ based on indicators selected as representative of the inspection carried out in decentralized offices. This scoring system – called Project Quality – is defined by three ‘‘synthetic indicators’’ determined periodically by the 92 Provincial Labour Directorates (in Italian: Direzioni Provinciali del Lavoro – DPL) operating in the country. It does indeed have a rating system that defines a ranking among the offices. This paper presents the results of the research in order to analytically describe the performance level with a different model and also suggesting the possible influence exerted by ‘‘local context variables’’, i.e., those relating to the geo-socio-economic differentials, in explaining the efficiency of inspection. The data are analyzed according to the variable inspection and local was formalized through a second-order structural equations model. Keywords: PLS Path-Modeling, Second Order Latent Variables, Performance Evaluation, Context Variables; Inspection Activity.

In this paper, we introduce a new method to improve the power of the chi-square test for goodness of fit (GOF) of logistic distribution under selective order ranked Set sampling (RSS) based on minimum, median and maximum as compared to simple random sampling (SRS). Based on a simulation study, we illustrate that the chi-square test is found to be more powerful under selective order RSS when compared to SRS, particularly for minimum and maximum. However, for the case of median RSS, the test is found to be more powerful under SRS. To investigate these results further, the Kullback- Leibler information (KLI) is applied and similar results are found. Keywords: Goodness of fit test, chi-square test, logistic distribution, ranked set sample, simple random sample.

We study the estimators of three financial performance measures: the Sharpe Ratio, the Mean Difference Ratio and the Mean Absolute Deviation Ratio. The analysis is performed under two sets of assumptions. First, the case of i.i.d. Normal returns is considered. After that, relaxing the normality assumption, the case of i.i.d. returns is investigated. In both situations, we study the bias of the estimators and we propose their bias-corrected version. The exact and asymptotic distribution of the three estimators is derived under the assumption of i.i.d. Normal returns. Concerning the case of i.i.d. returns, the asymptotic distribution of the estimators is provided. The latter distributions are used to define exact or asymptotic confidence intervals for the three indices. Finally, we perform a simulation study in order to assess the efficiency of the bias corrected estimators, the coverage accuracy and the length of the asymptotic confidence intervals. Keywords: Financial Performance Measure, Sharpe Ratio, Mean Difference Ratio, Mean Absolute Deviation Ratio, Concentration Measures, Statistical Analysis of Financial Data.

Non-Symmetric Correspondence Analysis-NSCA (D’Ambra and Lauro, 1989) is a useful technique for analyzing a two-way contingency table. There are many real-life applications where it is not appropriate to perform classical correspondence analysis because of the obvious asymmetry of the association between the variables. The key difference between the symmetrical and non-symmetrical versions of correspondence analysis rests on the measure of the association used to quantify the relationship between the variables. For a two-way, or multi-way, contingency table, the Pearson chisquared statistic is commonly used when it can be assumed that the categorical variables are symmetrically related. However, for a two-way table, it may be that one variable can be treated as a predictor variable and the second variable can be considered as a response variable. Yet, for such a variable structure, the Pearson chi-squared statistic is not an appropriate measure of the association. Instead, one may consider the Goodman-Kruskal tau index. In the case that there are more than two cross-classified variables, multivariate versions of the Goodman-Kruskal tau index can be considered. These include Marcotorchino’s index (Marcotorchino, 1985) and Gray-Williams’ index (Gray and Williams, 1975). In the present paper, the Multiple non- Symmetric Correspondence Analysis- MNSCA (Gray and Williams, J. S,1975), is used for the evaluation of the innovative performance of the manufacturing enterprises in Campania. Innovation represents a very important element for the competition of the enterprises and economic growth. Only the enterprises which are able to innovate regularly can have at their disposal a range of more and more appealing products for the customers. Moreover, only a constant innovation provides the constant efficiency of the processes and the optimization of the production costs. Finally, the use of the ellipse confidence has allowed to identify a category which is statistically significant. Keywords: CATANOVA, Confidence Ellipse, Gray-Williams Multiple Tau Index, Multiple Non Symmetrical Correspondence Analysis

In this paper we present a method for estimating the effect of college education independent of individual ability. We use a matching procedure to compare graduates and high school diploma holders (the latter to be used as counterfactuals) in order to identify both treatment and ability parameters in a two-regime equation model. A sensitivity analysis suggests that our matching results are robust with respect to a possible bias due to unobserved heterogeneity. Using Istat’s Survey on Italian Graduates, we estimate that the average effect of one year of college attendance on labour income is close to 7.5%. Unlike the results reported in recent literature, the effect of education is not higher for better endowed individuals. Keywords: Ability Bias, Matching, Treatment Effects Estimation, Two-Regime Regression Model.

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Applied Statistics is certainly devoted to extract information from any kind of data. Data which characterize objects of interest. Ranking, i.e. finding a complete order among objects, belongs to the tasks of Applied Statistics. Not anticipating a historical research, it seems, however, as if the task of ranking in terms of the theory of partially ordered sets does not play that role in statistics which it should do, taking into account the enormous multitude, diversity and popularity of ranking studies. The idea is simple, not to say trivial. Let objects x1, …, xn be characterized by m data, attributes, say qj(j = l, …, m), then xi1 < xi2 if and only if qj (xi1) = qj (xi2) for all j, and with at least one qj* with a strict inequality. It can be easily seen that this definition (being the basis of the ‘‘Hasse diagram technique’’ (HDT)) does not guarantee that every object is in a