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digital STATISTICA & APPLICAZIONI - 2006 - 1
Digital issue
issue 1 - 2006
publisher Vita e Pensiero
format Digital issue | Pdf
language English
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Primo fascicolo del 2006


A Nonlinear Least Squares Solution of a Minimax Estimation Problem for Stationary Time Series
by Aride Mazzali, Marica Manisera pages: 19 Download
The parameter estimation problem for the ARMA models is considered under a minimax approach: when the objective is to minimize the largest deviations in time series, it is useful to define a generalized version of a minimax estimator, minimizing the sum of the r-th powers of the k < n largest absolute deviations. The solution to that problem can be obtained by a searching procedure based on a grid of values on the admissible parametric space. The aim of this paper is propose a new procedure (called FINLS) to solve that minimax problem when a quadratic loss function is considered. FINLS approximates the searching procedure by a modified NLS method, with a filter matrix W selecting the largest absolute deviations to be included in the computation. Some applications account for the validity of the proposed estimation process. The results of a simulative study empirically show that the asymptotic properties of the NLS estimator could be extended to the proposed estimator. We also propose an asymptotic estimator for the covariance matrix of the FINLS estimated parameters.
On the problem of the minimal sample size for the ratio estimation: an Empirical Bayes approach
by Antonio Gambini, Enrico Di Bella pages: 11 Download
In many application contexts it may be useful to adopt a measure of pre-cision for the estimation of the proportion π of units belonging to a certain popula-tion having some definite characteristics taking into account the value of this un-known fraction. This work discusses the use of objective prior information, deriving from pre-test or pilot inquires, and the application of Empirical Bayes Procedures in the context of experimental sample design when there is the need for the definition of the minimal sufficient sampling size required to grant the desidered relative pre-cision.
Bipolar mean and mean deviation about the bipolar mean for discrete quantitative variables
by Walter Maffenini, Mariangela Zenga pages: 18 Download
Recently, Maffenini and Zenga (2005) have introduced, for the ordinal variables, the bipolar mean that can be seen as a frequencies distribution. In this paper, the bipolar mean has been extended to the discrete variables. Moreover for these variables it has been introduced a new variability measure: the mean deviation about the bipolar mean. It has been shown that, for the discrete variables, the mean deviation about the bipolar mean is less or equal to the mean deviation about the arithmetic mean. A new interpretation of the mean deviations in terms of “unitary steps” has been given too. Finally, the mean deviation about the bipolar mean can be considered as a Gini’s dissimilarity index.
Forensic Analysis and Statistics
by Julian A. Roach, Smail Mahdi pages: 17 Download
In this paper we present the development of forensic analysis and how Statistics has addressed the difficult areas of controversy in identifying individuals. The basic model of VNTR analysis of DNA evidence has succeeded conventional means of identification such as the use of blood groups and serum proteins. The su-periority of DNA methods has broadened its use in the forensic community however it is also heavily scrutinized statistically due to the probabilistic interpretation of compared samples as well as the difficulty posed by the large number of parameters in the model. As we discuss the methodologies and statistical models used to analyze forensic information from DNA we introduce a stochastic method that can be used to provide solutions to the common problems in forensic analysis.
A proposal for setting-up vulnerability indicators in the presence of missing data
by Pier Alda Ferrari, Paola Annoni, Sergio Urbisci pages: 15 Download
A procedure for the construction of an indicator in the presence of structured missing data is proposed. In particular, we face the problem of creating a ‘measure’ of the damage degree of valuable historical-architectonical buildings on the basis of the observation of several ordinal variables. Our proposal is the jointly use of Nonlinear PCA and an imputation method for missing data treatment.
The adopted procedure can be generally applied when an indicator is needed on the basis of the observation of ordinal, but also nominal or numerical, variables, which are deeply interrelated and are affected by systematic missing data. It has the nice feature of treating missing data according to the relevance of variables affected by missing observations and, at the same time, it preserves all the properties of Nonlinear PCA without missing data.
Furthermore, the method provides category quantifications and variable loadings that could be used for future inventory of buildings (in general of ‘units’) not included in the initial survey.
Un metodo non parametrico multi-aspetto per la valutazione dell’esperienza universitaria
by Marco Marozzi, Mario Bolzan pages: 16 Download
The University experience is central in the life of the young. Universities should provide a high level student support. To this end, a careful evaluation of university services is necessary. This evaluation is complex because it involves many aspects. Therefore, a multi-aspect nonparametric method which allows to combine several partial evaluations is used. The method is applied to data from a sample survey conducted on students of the University of Padova that are at the end of the study process. In the paper we consider the quality of many services, such as registrar’s offices, the structure of exams, student socialization and reached skills.