di Enrico Di Bella, Antonio Gambini
The game of the roulette has stimulated the creation of gambling strategies more than any other casino
game. The goal stated by many of these strategies is the overturning of the unfavourable condition
of the gambler guaranteeing a positive average return. Although well known in literature that
this result cannot be obtained, the decision of how and how much the player can bet allows the
maximization of the probability of some specific goal prearranged by the gambler. In this work
some of the most famous systems applied in casinos are analyzed and confronted. The availability
of the come ups of the numbers of a single roulette in the course of a solar year of a famous Italian
public casino, allows the verification of the unbiasedness of the wheel and the faithful adhesion of
the empirical come ups to those regarding the correspondent discrete uniform theoretical model.
di Francesco Chelli, Alberto Niccoli
The paper deals with the estimation of the attitude to risk of a group of people, the Board of the
Foundation for the Saving Bank of Florence. A specific method is used: the so-called trade-off method,
both with the outward and the inward procedure.
In a previous study Bacci and Chiandotto (2002) presented the data, holding that the risk attitude
for the Board implies propensity to risk when low levels of income and utility are concerned, and
risk aversion for higher values of income/utility.
Different theoretical utility functions are estimated in this paper: very simple ones, like the power utility
function, and more complex ones, including the specification used in Bacci and Chiandotto (2003).
Our results imply either risk neutrality (aversion), when so-called outward trade-off procedure (inward
trade-off procedure) data alone are used or, perhaps, risk aversion (propensity) when low
(high) values for income/utility are considered.
di Roberto Gismondi, Massimo Alfonso Russo
This work remarks the need to carefully evaluate the real importance of each variable used in a
multivariate analysis context, with particular regard to cases when an overall performance ranking
is the main final purpose. In particular, both a preliminary transformation of variables – aimed at
reducing asymmetry and variability of their variation ranges – and the evaluation of their intrinsic
explicative power – through redundancy analysis and weighting methods – are proposed. Theoretical
and empirical considerations are developed in the frame of quality of life evaluation, carried
out at the Italian provinces level on the basis of a yearly survey managed by the Italian economic
newspaper ‘‘Il Sole24ore’’. A particular emphasis is given to some normalisation criteria and the
case when original variables are grouped ‘‘a priori’’ into logical blocks. A final comparison between
the actual ranking method and a series of alternatives is proposed as well.
di Alessandro Zini
In this note a generalisation of the bipolar mean, recently introduced in the literature by Maffenini
and Zenga (2005), is presented and discussed. It seems interesting in those contexts, where the categories
of an ordinal variable are to be thought as ‘‘non equidistant’’, like in some problems in the
customer satisfaction analyses. It is pointed out that the particular bipolar mean chosen for a problem
can modify the ‘‘ordering’’ among the frequency distributions with fixed sum N.
di Sebastián Torcida, Nélida Winzer
Since first formulated, orthogonal Procrustes analysis has been mainly related to the biometrical
study of shapes (shape analysis) based on landmarks. Essentially, this is a method to superimpose
two configurations of points by means of a similarity – a combination of a translation term, an
isotropic change of scale and an orthogonal transformation – in order to produce an optimal fit, in
a least-squares sense. And among them, the problem of finding the best orthogonal transformation
has its own particular interest from a biological point of view and it is known as the Procrustes
rotation (PR) problem. In morphometrics, the presence of a particular type of symmetry often
constrains the search of the PR to be either a determinant 1 or a determinant -1 orthogonal matrix.
While the analytical solution to the first problem is well known, a formal proof of the solution to
the latter is still required. A common-analytical proof of the solution for both constrained PR
problems is given in this work, based on the standard (and unique) singular-value descomposition.
di Walter Maffenini
Being temporarily not at home can often cause the impossibility to give out a questionnaire to each
selected unit of a sample; moreover, a high percentage of nonrespondents can strongly affect the
quality of estimates. In order to solve this problem the ‘‘not at home’’ are usually called back until
they become available; however, this methodology highly increases the costs of a survey.
The main idea of this paper traces back to an estimation method early proposed by Politz and Simmons;
in particular, a new estimator, based on the regression method, is proposed, so that the auxiliary
information about the number of evenings spent at home by the units of the target population
can be used. The proposed estimator is shown to be unbiased and more efficient than the one based
only on the responses of the units being at home when first contacted. Moreover, unlike from the
Politz-Simmons estimator, the variance of the proposed estimator can be easily determined and
computed. Finally, in order to discuss the asymptotic properties of the regression estimator, the results
of some simulations are reported; both the proposed estimator and the Politz-Simmons one
turn out to be asymptotically unbiased; however, the regression estimator still proves to be more efficient.