Related papers: Nonstationary Gauss-Markov Processes: Parameter Es…

We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…

We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is…

In this work, we investigate Gaussian Mixture Models ({\it abbrv} GMM) and the related problem of non parametric maximum likelihood estimation ({\it abbrv} NPMLE) from the perspective of statistical mechanics. In particular, we establish…

We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model.…

In this paper, we consider the filtering and smoothing recursions in nonparametric finite state space hidden Markov models (HMMs) when the parameters of the model are unknown and replaced by estimators. We provide an explicit and time…

We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly…

This paper addresses distributed parameter estimation in randomized one-hidden-layer neural networks. A group of agents sequentially receive measurements of an unknown parameter that is only partially observable to them. In this paper, we…

We consider finite blocklength lossy compression of information sources whose components are independent but non-identically distributed. Crucially, Gaussian sources with memory and quadratic distortion can be cast in this form. We show…

This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…

In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…

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 extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…

This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…

We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the…

Finite state space hidden Markov models are flexible tools to model phenomena with complex time dependencies: any process distribution can be approximated by a hidden Markov model with enough hidden states.We consider the problem of…

We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of…

In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the…

In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…

Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…