Related papers: On nonparametric estimation of the interaction fun…
In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…
The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density…
In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a…
We present a new active learning algorithm based on nonparametric estimators of the regression function. Our investigation provides probabilistic bounds for the rates of convergence of the generalization error achievable by proposed method…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a…
We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims…
Despite the risk of misspecification they are tied to, parametric models continue to be used in statistical practice because they are accessible to all. In particular, efficient estimation procedures in parametric models are simple to…
The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical…
The purpose of the present work is to construct estimators for the random effects in a fractional diffusion model using a hybrid estimation method where we combine parametric and nonparametric thechniques. We precisely consider $n$…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…
Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid in time and space with infill asymptotics in…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…
We study the asymptotic error between the finite element solutions of nonlocal models with a bounded interaction neighborhood and the exact solution of the limiting local model. The limit corresponds to the case when the horizon parameter,…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…