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Modern statistical process monitoring (SPM) applications focus on profile monitoring, i.e., the monitoring of process quality characteristics that can be modeled as profiles, also known as functional data. Despite the large interest in the profile monitoring literature, there is still a lack of software to facilitate its practical application. This article introduces the funcharts R package that implements recent developments on the SPM of multivariate functional quality characteristics, possibly adjusted by the influence of additional variables, referred to as covariates. The package also implements the real-time version of all control charting procedures to monitor profiles partially observed up to an intermediate domain point. The package is illustrated both through its built-in data generator and a real-case study on the SPM of Ro-Pax ship CO2 emissions during navigation, which is based on the ShipNavigation data provided in the Supplementary Material.

The development of data acquisition systems is facilitating the collection of data that are apt to be modelled as functional data. In some applications, the interest lies in the identification of significant differences in group functional means defined by varying experimental conditions, which is known as functional analysis of variance (FANOVA). With real data, it is common that the sample under study is contaminated by some outliers, which can strongly bias the analysis. In this paper, we propose a new robust nonparametric functional ANOVA method (RoFANOVA) that reduces the weights of outlying functional data on the results of the analysis. It is implemented through a permutation test based on a test statistic obtained via a functional extension of the classical robust $ M $-estimator. By means of an extensive Monte Carlo simulation study, the proposed test is compared with some alternatives already presented in the literature, in both one-way and two-way designs. The performance of the RoFANOVA is demonstrated in the framework of a motivating real-case study in the field of additive manufacturing that deals with the analysis of spatter ejections. The RoFANOVA method is implemented in the R package rofanova, available online at https://github.com/unina-sfere/rofanova.

Georeferenced compositional data are prominent in many scientific fields and in spatial statistics. This work addresses the problem of proposing models and methods to analyze and predict, through kriging, this type of data. To this purpose, a novel class of transformations, named the Isometric $\alpha$-transformation ($\alpha$-IT), is proposed, which encompasses the traditional Isometric Log-Ratio (ILR) transformation. It is shown that the ILR is the limit case of the $\alpha$-IT as $\alpha$ tends to 0 and that $\alpha=1$ corresponds to a linear transformation of the data. Unlike the ILR, the proposed transformation accepts 0s in the compositions when $\alpha>0$. Maximum likelihood estimation of the parameter $\alpha$ is established. Prediction using kriging on $\alpha$-IT transformed data is validated on synthetic spatial compositional data, using prediction scores computed either in the geometry induced by the $\alpha$-IT, or in the simplex. Application to land cover data shows that the relative superiority of the various approaches w.r.t. a prediction objective depends on whether the compositions contained any zero component. When all components are positive, the limit cases (ILR or linear transformations) are optimal for none of the considered metrics. An intermediate geometry, corresponding to the $\alpha$-IT with maximum likelihood estimate, better describes the dataset in a geostatistical setting. When the amount of compositions with 0s is not negligible, some side-effects of the transformation gets amplified as $\alpha$ decreases, entailing poor kriging performances both within the $\alpha$-IT geometry and for metrics in the simplex., Comment: 31 pages and 13 Figures. Supplementary material with 3 Figures

The assessment of the vulnerability of a community endangered by seismic hazard is of paramount importance for planning a precision policy aimed at the prevention and reduction of its seismic risk. We aim at measuring the vulnerability of the Italian municipalities exposed to seismic hazard, by analyzing the open data offered by the Mappa dei Rischi dei Comuni Italiani provided by ISTAT, the Italian National Institute of Statistics. Encompassing the Index of Social and Material Vulnerability already computed by ISTAT, we also consider as referents of the latent social and material vulnerability of a community, its demographic dynamics and the age of the building stock where the community resides. Fusing the analyses of different indicators, within the context of seismic risk we offer a tentative ranking of the Italian municipalities in terms of their social and material vulnerability, together with differential profiles of their dominant fragilities which constitute the basis for planning precision policies aimed at seismic risk prevention and reduction., Comment: 23 page, 20 figures; abstract corrected

A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised definitions of marginal densities and the latter capturing the dependence between the two random variables being studied. The developed framework opens new perspectives for dependence modelling (which is commonly performed through copulas), and allows for the analysis of dataset of bivariate densities, in a Functional Data Analysis perspective. A spline representation for bivariate densities is also proposed, providing a computational cornerstone for the developed theory.

In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also on two real-data benchmark examples.

In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity. We show that the method can be used in a block sequential Gaussian simulation framework in order to assess the variability of downscaled quantities. Finally, to validate the method, we test it first in an idealized scenario and then apply it for the downscaling of digital soil maps on a more realistic case study. The digital soil maps for the realistic case study are obtained from SoilGrids, a system for automated soil mapping based on state-of-the-art spatial predictions methods.

Probability density functions (PDFs) can be understood as continuous compositions by the theory of Bayes spaces. The origin of a Bayes space is determined by a given reference measure. This can be easily changed through the well-known chain rule which has an impact on the geometry of the Bayes space. This work provides a mathematical framework for setting a reference measure. It is used to develop a weighting scheme on the bounded domain of distributional data. The impact on statistical analysis is shown from the perspective of simplicial functional principal component analysis. Moreover, a novel centered log-ratio transformation is proposed to map a weighted Bayes spaces into an unweighted $L^2$ space, enabling to use most tools developed in functional data analysis (e.g. clustering, regression analysis, etc.) while accounting for the weighting strategy. The potential of our proposal is shown through simulation and on a real case study using Italian income data., Comment: 28 pages, 10 figures

Data taking value on a Riemannian manifold and observed over a complex spatial domain are becoming more frequent in applications, e.g. in environmental sciences and in geoscience. The analysis of these data needs to rely on local models to account for the non stationarity of the generating random process, the non linearity of the manifold and the complex topology of the domain. In this paper, we propose to use a random domain decomposition approach to estimate an ensemble of local models and then to aggregate the predictions of the local models through Fr\'{e}chet averaging. The algorithm is introduced in complete generality and is valid for data belonging to any smooth Riemannian manifold but it is then described in details for the case of the manifold of positive definite matrices, the hypersphere and the Cholesky manifold. The predictive performance of the method are explored via simulation studies for covariance matrices and correlation matrices, where the Cholesky manifold geometry is used. Finally, the method is illustrated on an environmental dataset observed over the Chesapeake Bay (USA).