arXiv subjects

Francesca Torti

Publications and source records attributed to Francesca Torti.

4 recordsLinked to original sources

arXiv2026

Sentiment sensing: comparative analysis of multilingual sentiment dynamics

Cross-country sentiment analysis faces three fundamental challenges: language-specific biases distort comparisons, compositional data constraints invalidate standard statistics and temporal dynamics lack rigorous testing frameworks. We introduce sentiment sensing, a framework that addresses these gaps through integrated statistical methods. By combining compositional data analysis, functional data methods, and non-parametric inference, sentiment sensing enables valid multilingual comparisons and statistically defensible detection of sentiment shifts. Our framework has been tested in two case studies, analyzing news articles from the 27 countries of the European Union on the topics of energy and artificial intelligence. Sentiment sensing focuses on multilingual sentiment analysis enabling rigorous comparative science.

cs.CL↗

arXiv2026

Calibration of robust covariance estimation under heavy tails

The Minimum Covariance Determinant (MCD) estimator is one of the most widely used high-breakdown estimators of multivariate location and scatter. Its practical success relies on suitable corrections, which remove the asymptotic and small-sample biases introduced by trimming. While explicit consistency factors are available under the multivariate normal distribution and, more recently, under multivariate Student-t models, these corrections only address the asymptotic behavior of the estimator. In the Gaussian case, it is known showed that the MCD also exhibits a non-negligible finite-sample bias, particularly for small sample sizes and relatively large dimensions. Such bias propagates to robust Mahalanobis distances and may affect subsequent procedures, including multivariate outlier detection and robust inference. This paper investigates the finite-sample behavior of the MCD estimator and of the related robust distances under multivariate Student-t distributions, a potentially relevant scenario in many application fields. Extensive Monte Carlo experiments are carried out over a broad range of sample sizes, dimensions, trimming levels and degrees of freedom. Based on these experiments, empirical correction factors are obtained and approximated by smooth functions, providing a computationally efficient calibration suitable for practical implementations to heavy-tailed data. The proposed corrections are developed both for the scatter bias and the robust distance quantiles, thus leading to improved approximations for robust inference.

stat.ME↗

arXiv2026

Interactive and Robust PCA Graphics with FSDA in MATLAB

Principal Component Analysis (PCA) is a standard method for dimension reduction and the exploratory analysis of multivariate data, but a complete applied workflow often requires more than numerical eigenvectors and static plots. This article documents a set of routines in the FSDA toolbox for MATLAB that implements an integrated workflow for interactive and robust PCA graphics. The software contribution consists of coordinating classical SVD-based PCA, dynamic biplot scaling controlled by row and column parameters, score-distance and orthogonal-distance diagnostics, hard-trimming robust PCA through the Minimum Covariance Determinant and the Forward Search, linked brushing, geographical displays, and three-dimensional projection diagnostics. The implementation returns reproducible numerical output while also exposing graphical controls for changing biplot geometry, confidence regions, displayed labels, robust trimming levels, and linked selections. The methodology is illustrated on quality-of-life indicators for Italian provinces, where the software reveals variable groups, atypical provinces, robust and non-robust PCA structures, and geographical patterns. The emphasis is on statistical software: no new PCA estimator is proposed, but established PCA and robust-PCA methodology is combined in a documented, extensible, and script-reproducible MATLAB environment.

stat.ME↗

arXiv2023

A practically efficient fixed-pivot selection algorithm and its extensible MATLAB suite

Many statistical problems and applications require repeated computation of order statistics, such as the median, but most statistical and programming environments do not offer in their main distribution linear selection algorithms. We introduce one, formally equivalent to quickselect, which keeps the position of the pivot fixed. This makes the implementation simpler and much practical compared with the best known solutions. It also enables an "oracular" pivot position option that can reduce a lot the convergence time of certain statistical applications. We have extended the algorithm to weighted percentiles such as the weighted median, applicable to data associated with varying precision measurements, image filtering, descriptive statistics like the medcouple and for combining multiple predictors in boosting algorithms. We provide the new functions in MATLAB, C and R. We have packaged them in a broad MATLAB toolbox addressing robust statistical methods, many of which can be now optimised by means of efficient (weighted) selections.

stat.ME↗