Related papers: Consistency of MLE in partially observed diffusion…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic…
Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…
The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is based on a quasi-linear approach with prescribed inner and outer boundary conditions. The 1-d diffusion…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges…
In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
According to standard econometric theory, Maximum Likelihood estimation (MLE) is the efficient estimation choice, however, it is not always a feasible one. In network diffusion models with unobserved signal propagation, MLE requires…
In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the…
The problem of estimation of the distribution parameters on the sample when the part of these parameters are discrete (e.g. integer) is considered. We prove that the rate of convergence of MLE estimates under the natural conditions on the…
In this article, we introduce a novel non-parametric predictor, based on conditional expectation, for the unknown diffusion coefficient function $\sigma$ in the stochastic partial differential equation $Lu = \sigma(u)\dot{W}$, where $L$ is…
We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that maximum likelihood estimator is strongly consistent, if the scale parameters of the component uniform distributions are restricted from…
We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter…
Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…
This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…