Publications
2026
Stochastic Environmental Research and Risk Assessment
Abstract
Given samples of density functions on an interval (a, b) of $\mathbb R$, categorized according to a factor variable, we aim to test the equality of their mean functions both overall and across the groups defined by the factor. While the Functional Analysis of Variance (FANOVA) methodology is well-established for functional data, its adaptation to density functions (DANOVA) is necessary due to their inherent constraints of positivity and unit integral. To accommodate these constraints, we naturally use Bayes spaces methodology by mapping the densities using the centered log-ratio transformation into the $L^2_0 (a,b)$ space where we can use FANOVA techniques. Many traditional contrasts in FANOVA rely on squared differences and can be reinterpreted as squared distances between Bayes perturbations within the densities space. We illustrate our methodology on a dataset comprising daily maximum temperatures across Vietnamese provinces between 1987 and 2016. Within the context of climate change, we first investigate the existence of a non-zero temporal trend of the densities of daily maximum temperature over Vietnam and then examine whether there is any regional effect on these trends. Finally, we explore odds ratio based interpretations allowing to describe the trends more locally.
Journal of Multivariate Analysis
Abstract
Invariant coordinate selection (ICS) is a dimension reduction method, used as a preliminary step for clustering and outlier detection. It has been primarily applied to multivariate data. This work introduces a coordinate-free definition of ICS in an abstract Euclidean space and extends the method to complex data. Functional and distributional data are preprocessed into a finite-dimensional subspace. For example, in the framework of Bayes Hilbert spaces, distributional data are smoothed into compositional spline functions through the Maximum Penalised Likelihood method. We describe an outlier detection procedure for complex data and study the impact of some preprocessing parameters on the results. We compare our approach with other outlier detection methods through simulations, producing promising results in scenarios with a low proportion of outliers. ICS allows detecting abnormal climate events in a sample of daily maximum temperature distributions recorded across the provinces of Northern Vietnam between 1987 and 2016.
2023
Robust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler
Abstract
Invariant coordinate (or component) selection (ICS) is a multivariate statistical method introduced by Tyler et al. (J R Stat Soc Ser B (Stat Methodol) 71(3):549–592, 2009) and based on the simultaneous diagonalization of two scatter matrices. A model-based approach of ICS, called invariant coordinate analysis, has already been adapted for compositional data in Muehlmann et al. (Independent component analysis for compositional data. In Daouia, A, Ruiz-Gazen A (eds) Advances in Contemporary Statistics and Econometrics: Festschrift in Honor of Christine Thomas-Agnan. Springer, New York, pp. 525–545, 2021). In a model-free context, ICS is also helpful at identifying outliers Nordhausen and Ruiz-Gazen (J Multivar Anal 188:104844, 2022). We propose to develop a version of ICS for outlier detection in compositional data. This version is first introduced in coordinate space for a specific choice of isometric log-ratio coordinate system associated to a contrast matrix and follows the outlier detection procedure proposed by Archimbaud et al. (Comput Stat Data Anal 128:184–199, 2018a). We then show that the procedure is independent of the choice of contrast matrix and can be defined directly in the simplex. To do so, we establish some properties of the set of matrices satisfying the zero-sum property and introduce a simplex definition of the Mahalanobis distance and the one-step M-estimators class of scatter matrices. We also need to define the family of elliptical distributions in the simplex. We then show how to interpret the results directly in the simplex using two artificial datasets and a real dataset of market shares in the automobile industry.
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