Related papers: Deviation inequalities and moderate deviations for…
We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
Uncertain differential equations have a wide range of applications. How to obtain estimated values of unknown parameters in uncertain differential equations through observations has always been a subject of concern and research, many…
We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze…
In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…
We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary…
We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…
In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
Chirp signals are quite common in many natural and man-made systems like audio signals, sonar, radar etc. Estimation of the unknown parameters of a signal is a fundamental problem in statistical signal processing. Recently, Kundu and Nandi…
This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy noise, particularly when the sample paths are sparse. Specifically, given $n$…
A popular approach to perform inference on a target parameter in the presence of nuisance parameters is to construct estimating equations that are orthogonal to the nuisance parameters, in the sense that their expected first derivative is…
This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.)…
Consider a nonlinear regression model : y_{i}=g(x_{i},{\theta})+e_{i}, i=1,...,n, where the x_{i} are random predictors x_{i} and {\theta} is the unknown parameter vector ranging in a set {\Theta}\subsetR^{p}. All known results on the…
In a regression model with multiple response variables and multiple explanatory variables, if the difference of the mean vectors of the response variables for different values of explanatory variables is always in the direction of the first…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…