Related papers: Summary statistics for inhomogeneous marked point …
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the…
Many real-world objects can be modeled as a stream of events on the nodes of a graph. In this paper, we propose a class of graphical event models named temporal point process graphical models for representing the temporal dependencies among…
The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous…
We take a wavelet based approach to the analysis of point processes and the estimation of the first order intensity under a continuous time setting. A multiresolution analysis of a point process is formulated which motivates the definition…
We consider properties of the measurement intensity $\rho$ of a random variable for which the probability density function represented by the corresponding Wigner function attains negative values on a part of the domain. We consider a…
Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes,…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
We describe a simple test of the spatial uniformity of an ensemble of discrete events. Given an estimate for the point source luminosity function and an instrumental point spread function (PSF), a robust upper bound on the fractional point…
We study nonstationary intermittent dynamical systems, such as compositions of a (deterministic) sequence of Pomeau-Manneville maps. We prove two main results: sharp bounds on memory loss, including the "unexpected" faster rate for a large…
This paper considers maximum likelihood inference for a functional marked point process - the stochastic growth-interaction process - which is an extension of the spatio-temporal growth-interaction process to the stochastic mark setting. As…
We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a non asymptotic bound for the risk…
We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…
This study introduces an innovative local statistical moment approach for estimating Kramers-Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in…
Second-order statistics play a crucial role in analysing point processes. Previous research has specifically explored locally weighted second-order statistics for point processes, offering diagnostic tests in various spatial domains.…
We study multiple change-points detection using multi-samples tests based on U-statistics for absolutely regular observations. Our results extend those of Ngatchou-Wandji et al. (2022) concerned with the study of one single changepoint. The…
In this paper, we study the asymptotic distribution of some U-statistics whose entries are functions of empirical moments computed from non-overlapping consecutive blocks of an underlying weakly dependent process. The length of these blocks…
Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric $\bar{d}_1$ that combines…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…