New Trends in Functional Statistics and Related Fields

This volume gathers peer-reviewed contributions presented at the 6th International Workshop on Functional and Operatorial Statistics, IWFOS 2025, held in Novara, Italy, June 25-27, 2025.

Covering a broad spectrum of topics in functional and operatorial statistics and related fields, including high-dimensional statistics and machine learning, the contributions tackle both fundamental theoretical challenges and practical applications. A variety of features of statistics for functional data are addressed, such as estimation of functional features, exploration and pre-processing of functional data, methodologies for functional regression and forecasting problems, unsupervised and supervised classification, and testing procedures. Nonstandard functional data and situations which go beyond the pattern of samples of independent variables are investigated, and a link to the field of artificial intelligence is presented. Interesting real data applications to medicine, health, economics and the natural, environmental and social sciences are featured throughout.

Initiated at the University of Toulouse in 2008, the series of IWFOS workshops fosters discussion and international collaboration on theoretical advancements, methodological innovations, and applications in functional and operatorial statistics and related fields.

Chapter 42 is available open access under a Creative Commons Attribution 4. 0 International License via link. springer. com.

1 Germán Aneiros, Enea G. Bongiorno, Aldo Goia and Marie Hušková, An Introduction to the 6th Edition of the International Workshop on Functional and Operatorial Statistics. - 2 Nihan Acar-Denizli and Pedro Delicado, Local Constant Likelihood Estimation for Beta Distribution with Time Varying Parameters. - 3 Mohamed Alahiane, Mustapha Rachdi, Idir Ouassou and Philippe Vieu, An Expansion of the Functional Projection Pursuit Regression to Generalized Partially Linear Single Index Models. - 4 Alexander Aue, Sebastian Kühnert and Gregory Rice, On the Estimation of Invertible Functional Time Series. - 5 Patrick Bastian, Rupsa Basu and Holger Dette, Uniform Confidence Bands for Joint Angles Across Different Fatigue Phases. - 6 Sayan Bhadra and Anuj Srivastava, Scalar on Shape Regression Using Function Data. - 7 Filip Bo inec, Erik Mendroš and Stanislav Nagy, A Comparison of Band-based Approaches to Functional Depth. - 8 Enea G. Bongiorno, Lax Chan and Aldo Goia, Analysing the Complexity Mixture Structure of Daily Probability Densities of Bitcoin Returns. - 9 Teresa Bortolotti, Roberta Troilo, Alessandra Menafoglio and Simone Vantini, Regularized Nonparametric Estimation of Covariance Kernels for High-Dimensional Interferometric Data. - 10 Alain Boudou and Sylvie Viguier-Pla, Statistical Properties of a Random Series Transmitted by Filtering. - 11 Robert Cantwell and John Aston for the Alzheimer s Disease Neuroimaging Initiative, Multi-Object Regression: A Linear Framework via Partial Least Squares. - 12 Christian Capezza, Davide Forcina, Antonio Lepore, Biagio Palumbo, Monitoring the Covariance of Multichannel Profiles. - 13 Hervé Cardot and Caroline Peltier, Statistical Modeling of Categorical Trajectories with Multivariate Functional Data Approaches. - 14 Roberto Casarin, Radu Craiu and Qing Wang, Markov Switching Tensor Regressions. - 15 Michele Cavazzutti, Eleonora Arnone, Ying Sun, Marc G. Genton and Laura M. Sangalli, Functional Data Depth for the Analysis of Earth Surface Temperatures. - 16 Lax Chan, Laurent Delsol and Aldo Goia, Improving Finite Samples Performances in Nonparametric Functional Regression by Using Weighted Pseudo-Metrics. - 17 Aldo Clemente, Alessandro Palummo, Eleonora Arnone and Laura M. Sangalli, Smoothing with Nonlinear Partial Differential Equation Regularization. - 18 Adéla Czolková, Karel Hron and Sonja Greven, Functional Principal Component Analysis for Bivariate Densities and their Orthogonal Decomposition. - 19 Marco F. De Sanctis, Ilenia Di Battista, Eleonora Arnone, Cristian Castiglione, Mauro Bernardi, Francesca Ieva and Laura M. Sangalli, Estimating Multiple Quantile Surfaces: A Penalized Functional Approach. - 20 Simone Di Gregorio and Francesco Iafrate, Neural Drift Estimation for Ergodic Diffusions: Nonparametric Analysis and Numerical Exploration. - 21 Jacopo Di Iorio, Marzia A. Cremona and Francesca Chiaromonte, Amplitude-Invariant Functional Motif Discovery. - 22 Daniel Diz-Castro, Manuel Febrero-Bande and Wenceslao González-Manteiga, Testing the Significance of Covariates in Nonparametric Regression without the Curse of Dimensionality. - 23 Patric Dolmeta and Matteo Giordano, Gaussian Process Methods for Covariate-Based Intensity Estimation. - 24 Mélanie Dreina, Sylvie Viguier-Pla and Stéphane Abide, Spectral Analysis of Multidimensional Thermal Fields. - 25 Matteo Farnè and Xuanye Dai, Forecasting Dynamic Factor Scores by UNALSE Spectral Density Matrix Estimator. - 26 Manuel Febrero-Bande, Pedro Galeano and Wenceslao González-Manteiga, Testing for Linearity and Independence in Scalar-on-Function Regression with Responses Missing at Random by Generalized Distance Covariance. - 27 Antonino Gagliano, Chiara Di Maria, Gianluca Sottile, Sarah Beutler-Traktovenko, Luigi Augugliaro and Valeria Vitelli, A Novel Spectral Density Operator Approach to Unveil Dynamic Time Dependencies in Multivariate Long-Term ECGs. - 28 Nouhaila Goujili, Matthieu Saumard and Maher Jridi, Comparison of Deep Learning Methods for Functional Data. - 29 Nicolás Hernández and Stanislav Nagy, The Common Support Function with Applications. - 30 Karel Hron, Multivariate Densities in Bayes Spaces: The Novel Concept of Marginals and Its Implications. - 31 Šárka Hudecová, Daniel Hlubinka and Zden k Hlávka, Functional Sample Problem via Multivariate Optimal Measure Transport-Based Permutation Test. - 32 Marie Hušková and Charl Pretorius, Sequential Monitoring for Detection of Breaks in Panel Data. - 33 Ioannis Kalogridis and Stefan Van Aelst, Robust Penalized Splines for Location Estimation from Discretely Sampled Functional Data. - 34 Yuwei Jiang and Natalya Pya Arnqvist, Functional Regression with Shape Constraints. - 35 Francesca Ieva, Nicole Fontana, Carlo Andrea Pivato, Emanuele Di Angelantonio and Piercesare Secchi, Enhancing Causal Inference in Functional Data: a Method for Estimating Time-Varying Causal Treatment Effects. - 36 Luigi Ippoliti, Tonio Di Battista, Luigi Di Carlo, Stefania Fensore, Eugenia Nissi, Pasquale Valentini, Carlo Zaccardi, Linear and Nonlinear Regression Models for Spatial Downscaling of Particulate Matter. - 37 Alessandro Lanteri, Raffaele Argiento, Silvia Montagna, A Bayesian Non-Parametric Model to Learn Functions with Discontinuties. - 38 Salvatore Latora, Luigi Augugliaro and Gerda Claeskens, A Novel Approach To Estimate Functional Gaussian Graphical Model Based On Penalized Multivariate Functional Regression Model. - 39 Niels Lundtorp Olsen, Alessia Pini and Simone Vantini, Local Null Hypothesis Significance Testing on Riemaniann Manifolds. - 40 Hassan Maatouk, Didier Rullière and Xavier Bay, Efficient Bayesian Linear Models for a Large Number of Observations- 41 Jitka Machalová and Jana Heckenbergerová, Innovative Approach to Wind Direction Data Analyses: A Compositional Periodic Spline Representation in Bayes Spaces. - 42 Eva-Maria Maier, Alexander Fottner, Almond Stöcker and Sonja Greven, Bayes Hilbert Space Additive Density-on-Scalar Regression Based on Individual Observations. - 43 Terence Kevin Manfoumbi Djonguet and Guy Martial Nkiet, A Kernel-Based Approach for Testing Mutual Independence of Several Functional Variables. - 44 Alejandra Mercedes Martínez, Addressing Robustness and Sparsity in Partially Linear Additive Models. - 45 Valentina Masarotto and Yiya Chen, Covariance Operators for Phonetics: Revisiting Tonal Coarticulation. - 46 Caterina May, Theodoros Ladas, Davide Pigoli and Kalliopi Mylona, A-optimal Designs of Experiments in Linear Models with Dynamic Factors and Functional Responses. - 47 Alessandra Menafoglio, Moving Object-Oriented Spatial Statistics Beyond Stationary and Euclidean Paradigms. - 48 Erik Mendroš and Stanislav Nagy, The Spherical Depth for Functional Data. - 49 Tomáš Mrkvi ka, False Discovery Rate Envelope and its Performance for Local Testing in Functional Data Analysis. - 50 Stanislav Nagy, Interpretable Functional Boxplots. - 51 Silvia Novo, Alessandro Palummo and Laura M. Sangalli, Scalar-on-Function Regression with Partially Observed Covariate. - 52 Alessandro Palummo, Eleonora Arnone, Letizia Clementi and Laura M. Sangalli, Efficient Physics-Informed Smoothing of Space-time Functional Data. - 53 Giulia Patanè, Federica Nicolussi, Alexander Krauth, Günter Gauglitz, Bianca Maria Colosimo, Luca Dede and Alessandra Menafoglio, Ordinal-on-Function Dimensionality Reduction. - 54 Nicola Pronello, Rosaria Ignaccolo and Luigi Ippoliti, Varying Coefficient Regression Models on Fluvial Networks. - 55 Hedvika Ranošová and Daniel Hlubinka, Non-Parametric Testing of Time Reversibility in Functional Data. - 56 María D. Ruiz Medina and Rosa M. Crujeiras, An LRD Spectral Test for Irregularly Discretely Observed Functional Time Series in Manifolds. - 57 Diego Serrano and Eduardo García-Portugués, Prediction Regions for Functional-Valued Random Forests. - 58 Mohammad Reza Seydi, Johan Strandberg, Todd C. Pataky, and Lina Schelin, Sample Size Estimation for Two-Sample Functional Hypothesis Test. - 59 Han Lin Shang, Forecasting Age Distribution of Deaths at Subnational Level. - 60 Stanislav Škor a and Jitka Machalová, Statistical Analysis of Bivariate Densities with Compositional Splines. - 61 Veronika Šmajserová and Jitka Machalová, Prediction with Mixed Effects Smooth Models by using P-Splines. - 62 Marco Stefanucci, Mauro Bernardi and Antonio Canale, Locally Sparse Estimation for Functional Linear Models with Scalar Response. - 63 Shahin Tavakoli, Gilles Nisol, and Marc Hallin, Factor Models for High-Dimensional Functional Time Series. - 64 Romain Valla, Pavlo Mozharovskyi, and Florence d Alché-Buc, Anomaly-Driven Visualization of Functional Data. - 65 Simone Vantini, Leveraging Data Exchangeability for a More Reliable and Interpretable Functional Data Analysis. - 66 Marc Vidal, A Family of Moment Operators for Functional Data and Its Discriminative Properties.