MaxSkew and MultiSkew: Two R Packages for Detecting, Measuring and Removing Multivariate Skewness

Skewness plays a relevant role in several multivariate statistical techniques. Sometimes it is used to recover data features, as in cluster analysis. In other circumstances, skewness impairs the performances of statistical methods, as in the Hotelling's one-sample test. In both cases, there is the need to check the symmetry of the underlying distribution, either by visual inspection or by formal testing. The R packages MaxSkew and MultiSkew address these issues by measuring, testing and removing skewness from multivariate data. Skewness is assessed by the third multivariate cumulant and its functions. The hypothesis of symmetry is tested either nonparametrically, with the bootstrap, or parametrically, under the normality assumption. Skewness is removed or at least alleviated by projecting the data onto appropriate linear subspaces. Usages of MaxSkew and MultiSkew are illustrated with the Iris dataset

Sampling Distribution of the Gini Index from a Skew Normal

The Gini concentration ratio has been extensively used in the study of "inequality" of distributions. According to Chakrabarthy (1982), "the Lorenz curve and the Gini index have remained the most popular and powerful tool in the analyses of size distribution of income". A major statistical limitation of Gini Concentration Ratio is the absence and the intractability of appropriate sampling distribution (Hart, 1971, Nigard Sandstrom, 1981) We find that the exact sampling distribution of the Gini Concentration Index for a sample from a Skew Normal population has an Extended Skew Normal distribution. This result can be easily particularized to the normal case.Skew Normal, L-statistics, Small Sample, Gini Concentration Ratio, Exact Distribution.

On the exact sampling distribution of L-statistics

This paper shows that linear functions of order statistics (L-statistics) based on random samples have a Fundamental Skew distribution (Arellano-Valle Genton, 2003). The paper also examines the exact distribution of L-statistics when the sampled population is Skew Normal. Exact distributions of L-statistics from normal samples easily follows as special case.

Statistical Analysis of the Correlation between Italian and U.S. Stock Returns

An estimator of the correlation between Italian and U.S. Stock Returns is introduced. The properties of the estimator are invariant with respect to a wide class of GARCH models. The empirical evidence shows the existence of a positive correlation between Italian an U. S. stock returns.GARCH models, Invariance, Stock Returns.

Neither left nor right: Crisis, Wane of Politics, and the Struggles for Sovereignty

When I arrived for fieldwork in Rome, in early 2008, I was seeking to track and interview the ex- militants of the fascism-inspired ‘Spontaneista groups’. Active in the late 70s, these had been very violent and had claimed to be ‘neither left nor right’. Their name made reference to the supposed ‘spontaneity’ of their constitution and action, announcing an ideological predilection of instincts and drives over reason and thought. All of these movements had a short life of four to six years between the late 70s and the early 80s. I was then very surprised when – on my arrival in Rome – I ran into a crowd of students, dressed in black and with shaved heads, rallying against the reform of lower education and crying in the streets the slogan: ‘Non rossi, né neri, ma liberi pensieri

Linear transformations to symmetry

Abstract We obtain random vectors with null third-order cumulants by projecting the data onto appropriate subspaces. Statistical applications include, but are not limited to, the robustification of Hotelling's T 2 test against nonnormality. Our approach only requires the existence of the third-order moments and leads to normal transformed variables when the parent distribution belongs to well-known classes of sample selection models

What Can Anthropology Say about Populism?

In a recent article in Anthropology News, Víctor Giménez Aliaga suggests that the contemporary wave of populism calls for closer anthropological analysis of the term and its usages. While it is less interesting to me to partake in the eternal strive to define “what populism means,” I concur with Giménez Aliaga with the need for anthropology to asses “practices—that is, the ways and purposes with which the term is used in the political arena. In response to Gimenéz Aliaga’s call, I will try to sketch out some of the insights an anthropological perspective could provide around current political transformations

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew tt distribution

A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew $t$ density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.Comment: full-length version of the published paper, 31 pages with 9 figure

Canonical correlations and nonlinear dependencies

Canonical correlation analysis (CCA) is the default method for investigating the linear dependence structure between two random vectors, but it might not detect nonlinear dependencies. This paper models the nonlinear dependencies between two random vectors by the perturbed independence distribution, a multivariate semiparametric model where CCA provides an insight into their nonlinear dependence structure. The paper also investigates some of its probabilistic and inferential properties, including marginal and conditional distributions, nonlinear transformations, maximum likelihood estimation and independence testing. Perturbed independence distributions are closely related to skew-symmetric ones

Students’ Self-Organization of the Learning Environment during a Blended Knowledge Creation Course

Learner-centered blended learning approaches, such as Knowledge Creation, emphasize the self-organizing characteristic of thought and action, and value the students’ autonomy and self-regulation during the engagement in collaborative learning tasks. In blended contexts, the students need to organize their learning paths within a complex environment, including multiple online and offline learning spaces. This process of self-organization during courses based on the Knowledge Creation approach is currently an overlooked topic of research. The present case study is aimed at addressing this research gap by providing an in-depth understanding of the collaborative self-organization of a group of five undergraduate students participating in an interdisciplinary media design course. The course was designed according to the Knowledge Creation approach and was carried out before the start of the COVID-19 pandemic. The dialogical theory of the chronotope and the theory of cultural models constitute the main theoretical tools for the research. We used qualitative methods inspired by ethnography, including participant observation, in addition to the collection and analysis of audio-visual records, stimulated recall interviews, and learning diaries completed by the students. The findings show that the group self-organization changed across different phases of the collaborative task and involved the development of specific practices of self-organization. Cultural models associated with the task contributed to determine the students’ choices related to self-organization