Related papers: Maximum likelihood estimation for small noise mult…
We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only…
We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We address the estimation of the variance parameter and the estimation of…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…
We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…
It is shown that the intensity quantum noise of a single-emitter nanolaser can be accurately computed by adopting a stochastic interpretation of the standard rate equation model under the only assumption that the emitter excitation and…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
This paper considers estimating the parameters in a regime-switching stochastic differential equation(SDE) driven by Normal Inverse Gaussian(NIG) noise. The model under consideration incorporates a continuous-time finite state Markov chain…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…
In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
The problem of estimating a spiked covariance matrix in high dimensions under Frobenius loss, and the parallel problem of estimating the noise in spiked PCA is investigated. We propose an estimator of the noise parameter by minimizing an…
We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a…
We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…