arXiv subjects

Felix Cheysson

Publications and source records attributed to Felix Cheysson.

4 recordsLinked to original sources

arXiv2026

Ridge-penalised spectral least-squares estimation for point processes

Penalised estimation methods for point processes usually rely on a large amount of independent repetitions for cross-validation purposes. However, in the case of a single realisation of the process, existing cross-validation methods may be impractical depending on the chosen model. To overcome this issue, this paper presents a Ridge-penalised spectral least-squares estimation method for second-order stationary point processes. This is achieved through two novel approaches: a p-thinning-based cross-validation method to tune the penalisation parameter, relying on the spectral representation of the process; and the introduction of a spectral least-squares contrast based around the asymptotic properties of the periodogram of the sample. The proposed method is then illustrated by a simulation study on linear Hawkes processes in the context of parametric estimation, highlighting its performances against more traditional approaches, specifically when working with short observation windows.

stat.ME↗

arXiv2024

Spectral analysis for the inference of noisy Hawkes processes

Classic estimation methods for Hawkes processes rely on the assumption that observed event times are indeed a realisation of a Hawkes process, without considering any potential perturbation of the model. However, in practice, observations are often altered by some noise, the form of which depends on the context. It is then required to model the alteration mechanism in order to infer accurately such a noisy Hawkes process. While several models exist, we consider, in this work, the observations to be the indistinguishable union of event times coming from a Hawkes process and from an independent Poisson process. Since standard inference methods (such as maximum likelihood or Expectation-Maximisation) are either unworkable or numerically prohibitive in this context, we propose an estimation procedure based on the spectral analysis of second order properties of the noisy Hawkes process. Novel results include sufficient conditions for identifiability of the ensuing statistical model with exponential interaction functions for both univariate and bivariate processes, along with consistency and asymptotic normality guarantees of our estimator in the univariate case. Although we mainly focus on the exponential scenario, other types of kernels are investigated and discussed. A new estimator based on maximising the spectral log-likelihood is then described, and its behaviour is numerically illustrated on both synthetic data and neuronal data. Besides being free from knowing the source of each observed time (Hawkes or Poisson process), the proposed estimator is shown to perform accurately in estimating both processes.

stat.ME↗

arXiv2023

Mixing properties for multivariate Hawkes processes

Properties of strong mixing have been established for the stationary linear Hawkes process in the univariate case, and can serve as a basis for statistical applications. In this paper, we provide the technical arguments needed to extend the proof to the multivariate case. We illustrate these properties by establishing a functional central limit theorem for multivariate Hawkes processes.

math.ST↗

arXiv2020

Spectral estimation of Hawkes processes from count data

This paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood are not feasible. We show that spectral estimation based on Whittle's method is adapted to this case and provides consistent and asymptotically normal estimators, provided a mild moment condition on the reproduction function. Simulated datasets and a case-study illustrate the performances of the estimation, notably of the reproduction function even when time intervals are relatively large.

math.ST↗