Related papers: Approximate discrete-time schemes for the estimati…
We study the problem of parameters estimation in Indirect Observability contexts, where $X_t \in R^r$ is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates.…
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
We propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the…
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…
This paper presents two schemes to jointly estimate parameters and states of discrete-time nonlinear systems in the presence of bounded disturbances and noise and where the parameters belong to a known compact set. The schemes are based on…
Partially-observed data collected by sampling methods is often being studied to obtain the characteristics of information diffusion networks. However, these methods usually do not consider the behavior of diffusion process. In this paper,…
Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…
Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…