arXiv subjects

Matthieu Bulté

Publications and source records attributed to Matthieu Bulté.

5 recordsLinked to original sources

arXiv2025

Isotropic randomization for one-sample testing in metric spaces

We address the problem of testing hypotheses about a specific value of the Fréchet mean in metric spaces, extending classical mean testing from Euclidean spaces to more general settings. We extend an Euclidean testing procedure progresively, starting with test construction in Riemannian manifolds, leveraging their natural geometric structure through exponential and logarithm maps, and then extend to general metric spaces through the introduction of admissible randomization techniques. This approach preserves essential geometric properties required for valid statistical inference while maintaining broad applicability. We establish theoretical guarantees for our testing procedure and demonstrate its effectiveness through numerical experiments across different metric spaces and distributional settings. The practical utility of our method is further illustrated through an application to wind data in western Denmark, showcasing its relevance for real-world statistical analysis.

stat.ME↗

arXiv2024

An Autoregressive Model for Time Series of Random Objects

Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature that is predominantly non-parametric and model-free. To address this gap in models for time series of random objects, we introduce an adaptation of the classical linear autoregressive model tailored for data lying in a Hadamard space. The parameters of interest in this model are the Fréchet mean and a concentration parameter, both of which we prove can be consistently estimated from data. Additionally, we propose a test statistic for the hypothesis of absence of serial correlation and establish its asymptotic normality. Finally, we use a permutation-based procedure to obtain critical values for the test statistic under the null hypothesis. Theoretical results of our method, including the convergence of the estimators as well as the size and power of the test, are illustrated through simulations, and the utility of the model is demonstrated by an analysis of a time series of consumer inflation expectations.

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arXiv2023

Medoid splits for efficient random forests in metric spaces

This paper revisits an adaptation of the random forest algorithm for Fréchet regression, addressing the challenge of regression in the context of random objects in metric spaces. Recognizing the limitations of previous approaches, we introduce a new splitting rule that circumvents the computationally expensive operation of Fréchet means by substituting with a medoid-based approach. We validate this approach by demonstrating its asymptotic equivalence to Fréchet mean-based procedures and establish the consistency of the associated regression estimator. The paper provides a sound theoretical framework and a more efficient computational approach to Fréchet regression, broadening its application to non-standard data types and complex use cases.

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arXiv2021

Scalable Econometrics on Big Data -- The Logistic Regression on Spark

Extra-large datasets are becoming increasingly accessible, and computing tools designed to handle huge amount of data efficiently are democratizing rapidly. However, conventional statistical and econometric tools are still lacking fluency when dealing with such large datasets. This paper dives into econometrics on big datasets, specifically focusing on the logistic regression on Spark. We review the robustness of the functions available in Spark to fit logistic regression and introduce a package that we developed in PySpark which returns the statistical summary of the logistic regression, necessary for statistical inference.

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arXiv2019

A practical example for the non-linear Bayesian filtering of model parameters

In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential Importance Sampling (SIS) and Sequential Monte Carlo (SMC). Throughout the paper we illustrate the concepts and techniques with a practical example using real-world data. The task is to estimate the gravitational acceleration of the Earth $g$ by using observations collected from a simple pendulum. Importantly, the particle filters enable the adaptive updating of the estimate for $g$ as new observations become available. For tutorial purposes we provide the data set and a Python implementation of the particle filters.

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