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Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity…

Statistics Theory · Mathematics 2010-11-15 Cheng-Der Fuh

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Statistics Theory · Mathematics 2017-12-05 Shogo H. Nakakita , Masayuki Uchida

We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…

Statistics Theory · Mathematics 2025-03-31 Shohei Nakajima

Flow Matching (FM) models achieve remarkable results in generative tasks. Building upon diffusion models, FM's simulation-free training paradigm enables simplicity and efficiency but introduces a train-inference gap: model outputs cannot be…

Machine Learning · Computer Science 2026-01-30 Zhaoyi Li , Jingtao Ding , Yong Li , Shihua Li

We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…

Methodology · Statistics 2025-07-01 Hansheng Jiang , Adityanand Guntuboyina

We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…

Statistics Theory · Mathematics 2012-07-24 Stephen E. Fienberg , Alessandro Rinaldo

In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially…

Computation · Statistics 2023-09-20 Elsiddig Awadelkarim , Ajay Jasra , Hamza Ruzayqat

Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…

Statistics Theory · Mathematics 2018-05-16 Mathias Drton , Christopher Fox , Andreas Käufl , Guillaume Pouliot

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…

Probability · Mathematics 2014-05-13 Mikael Falconnet , Dasha Loukianova , Arnaud Gloter

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…

Statistics Theory · Mathematics 2016-01-27 David Dereudre , Frédéric Lavancier

We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove…

Statistics Theory · Mathematics 2018-10-02 Manuel Diehn , Axel Munk , Daniel Rudolf

This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor…

Computation · Statistics 2019-09-30 Rui Zhou , Junyan Liu , Sandeep Kumar , Daniel P. Palomar

We derive and prove the path-kernel formula for the linear response (parameter-derivative of averaged statistics) of SDEs. The parameter may affect the drift coefficient, the diffusion coefficient, and the initial condition. The formula…

Probability · Mathematics 2026-05-01 Angxiu Ni

The work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct…

Probability · Mathematics 2020-06-03 Meiqi Liu , Huijie Qiao

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…

Statistics Theory · Mathematics 2022-05-04 Han Yuecai , Zhang Dingwen

Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…

Computation · Statistics 2019-06-28 Minwoo Chae , Ryan Martin , Stephen G. Walker

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…

Statistics Theory · Mathematics 2010-08-18 Jimmy Olsson , Jonas Ströjby

We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…

Probability · Mathematics 2015-08-04 David Baños , Paul Krühner

In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum…

Statistics Theory · Mathematics 2011-11-09 Kentaro Tanaka

We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for…

Probability · Mathematics 2016-06-16 Siragan Gailus , Konstantinos Spiliopoulos