Related papers: Low-Rank and Sparse Drift Estimation for High-Dime…

While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…

We study the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt…

The problem of drift estimation for the solution $X$ of a stochastic differential equation with L\'evy-type jumps is considered under discrete high-frequency observations with a growing observation window. An efficient and asymptotically…

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse…

By using the existing sharp estimates of density function for rotationally invariant symmetric $\alpha$-stable L\'{e}vy processes and rotationally invariant symmetric truncated $\alpha$-stable L\'{e}vy processes, we obtain that Harnack…

This study examines a nonparametric inference on a stationary L\'evy-driven Ornstein-Uhlenbeck (OU) process $X = (X_{t})_{t \geq 0}$ with a compound Poisson subordinator. We propose a new spectral estimator for the L\'evy measure of the…

Fractional Ornstein-Uhlenbeck process of the second kind $(\text{fOU}_{2})$ is solution of the Langevin equation $\mathrm{d}X_t = -\theta X_t\,\mathrm{d}t+\mathrm{d}Y_t^{(1)}, \ \theta >0$ with Gaussian driving noise $ Y_t^{(1)} := \int^t_0…

This paper focuses on the identification of graphical autoregressive models with dynamical latent variables. The dynamical structure of latent variables is described by a matrix polynomial transfer function. Taking account of the sparse…

Conditions are given, sufficient for the distribution of an Ornstein-Uhlenbeck process with L\'evy noise to be absolutely continuous or to possess a smooth density. For the processes with non-degenerate drift coefficient, these conditions…

We consider the parametric estimation of the Ornstein-Uhlenbeck process driven by a non-Gaussian $\alpha$-stable L\'{e}vy process with the stable index $\alpha>1$ and possibly skewed jumps, based on a discrete-time sample over a fixed…

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…

The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to…

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low…

This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…

In this paper, we consider the statistical inference of the drift parameter $\theta$ of non-ergodic Ornstein-Uhlenbeck~(O-U) process driven by a general Gaussian process $(G_t)_{t\ge 0}$. When $H \in (0, \frac 12) \cup (\frac 12,1) $ the…

We consider estimation of the drift parameter $\vartheta>0$ in a \emph{partially observed} Ornstein--Uhlenbeck type model driven by a mixed fractional Brownian noise. Our framework extends the partially observed model of…

The question of existence and properties of stationary solutions to Langevin equations driven by noise processes with stationary increments is discussed, with particular focus on noise processes of pseudo-moving-average type. On account of…

We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter $H \in (0,1)$. We first focus on continuous observations and develop a kernel-based estimator achieving faster…

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…

This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy noise, particularly when the sample paths are sparse. Specifically, given $n$…