Related papers: Statistical Inference for Perturbed Multiscale Dyn…

Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…

We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the…

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…

The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems…

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…

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…

We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…

We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter…

The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many…

We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…

The aim of this paper is to study the asymptotic properties of the maximum likelihood estimator (MLE) of the drift coefficient for fractional stochastic heat equation driven by an additive space-time noise. We consider the traditional for…

Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and…

We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…

A statistical model is said to be un-normalised when its likelihood function involves an intractable normalising constant. Two popular methods for parameter inference for these models are MC-MLE (Monte Carlo maximum likelihood estimation),…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…

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…