Related papers: Moderate deviations for parameters estimation in a…
We study asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations of the log-price process. We distinguish three cases: subcritical (also called ergodic), critical and supercritical. In…
The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…
We investigate the problem of estimating the drift parameter of a high-dimensional L\'evy-driven Ornstein--Uhlenbeck process under sparsity constraints. It is shown that both Lasso and Slope estimators achieve the minimax optimal rate of…
We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…
Our goal is to establish large deviations and concentration inequalities for the maximum likelihood estimator of the drift parameter of the Ornstein-Uhlenbeck process without tears. We propose a new strategy to establish large deviation…
Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive…
We establish a moderate deviations principle (MDP) for the log-determinant $\log | \det (M_n) |$ of a Wigner matrix $M_n$ matching four moments with either the GUE or GOE ensemble. Further we establish Cram\'er--type moderate deviations and…
Let the Ornstein-Uhlenbeck process $(X_t)_{t\ge0}$ driven by a fractional Brownian motion $B^{H }$, described by $dX_t = -\theta X_t dt + \sigma dB_t^{H }$ be observed at discrete time instants $t_k=kh$, $k=0, 1, 2, \cdots, 2n+2 $. We…
In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale…
We propose a minimum distance estimator (MDE) for parameter identification in misspecified models characterized by a sequence of ergodic stochastic processes that converge weakly to the model of interest. The data is generated by the…
This paper deals with the Local Asymptotical normality for the joint drift parameter and Hurst parameter $H>3/4$ in the mixed fractional Ornstein-Uhlenbeck process. Different from the only estimation of the drift parameter when $H$ is…
We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…
This paper proposes consistent and asymptotically Gaussian estimators for the drift, the diffusion coefficient and the Hurst exponent of the discretely observed fractional Ornstein-Uhlenbeck process. For the estimation of the drift, the…
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 define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…