Related papers: Statistical inference for a partially observed int…
Permutation tests have been proposed by Albert et al. (2015) to detect dependence between point processes, modeling in particular spike trains, that is the time occurrences of action potentials emitted by neurons. Our present work focuses…
Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification.…
Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information measures to detect…
We introduce a new method for online parameter estimation in stochastic interacting particle systems, based on continuous observation of a small number of particles from the system. Our method recursively updates the model parameters using…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
This paper proposes a novel approach for semiparametric inference on the number $s$ of common trends and their loading matrix $\psi$ in $I(1)/I(0)$ systems. It combines functional approximation of limits of random walks and canonical…
We study a dynamical system modeling the Theory of Planned Behavior (TPB) in which each individual's behavioral intention evolves continuously under an ODE driven by internal attitudes, perceived social norms, and perceived behavioral…
Multivariate point processes are widely applied to model event-type data such as natural disasters, online message exchanges, financial transactions or neuronal spike trains. One very popular point process model in which the probability of…
We study the general fragmentation process starting from one element of size unity (E=1). At each elementary step, each existing element of size $E$ can be fragmented into $k\,(\ge 2)$ elements with probability $p_k$. From the continuous…
An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive…
When the number of subjects, $n$, is large, paired comparisons are often sparse. Here, we study statistical inference in a class of paired comparison models parameterized by a set of merit parameters, under an Erd\"{o}s--R\'{e}nyi…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…
As a tool for capturing irregular temporal dependencies (rather than resorting to binning temporal observations to construct time series), Hawkes processes with exponential decay have seen widespread adoption across many application…
We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This…
We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…
Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…
We consider a sequence of Hawkes processes whose excitation measures may depend on the generation, and study its scaling limits in the near-unstable limiting regime. The limiting random measures, characterized via a nonlinear convolutional…
In this paper, we consider a one-dimensional diffusion process with jumps driven by a Hawkes process. We are interested in the estimations of the volatility function and of the jump function from discrete high-frequency observations in a…
Denote by $p(k)$ the limit, as $n \rightarrow \infty$, of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$. We give an asymptotic formula for $p(k)$, showing that it is asymptotically…