Related papers: A Finite-Sample Deviation Bound for Stable Autoreg…
This study utilized the Gaussian Processes (GPs) regression framework to establish stochastic error bounds between the actual and predicted state evolution of nonlinear systems. These systems are embedded in the linear parameter-varying…
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the…
We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…
This paper is about vector autoregressive-moving average (VARMA) models with time-dependent coefficients to represent non-stationary time series. Contrarily to other papers in the univariate case, the coefficients depend on time but not on…
One problem of wide interest involves estimating expected crossing-times. Several tools have been developed to solve this problem beginning with the works of Wald and the theory of sequential analysis. An extension of his approach is…
Linear two-timescale stochastic approximation (SA) scheme is an important class of algorithms which has become popular in reinforcement learning (RL), particularly for the policy evaluation problem. Recently, a number of works have been…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
The G\"artner-Ellis condition for the square of an asymptotically stationary Gaussian process is established. The same limit holds for the conditional distri-bution given any fixed initial point, which entails weak multiplicative…
Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency. For a fixed stepsize, the iterates typically admit a stationary distribution that is rarely tractable. Prior work shows that as the…
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…
We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy…
We show a decomposition into the sum of a martingale and a deterministic quantity for time averages of the solutions to non-autonomous SDEs and for discrete-time Markov processes. In the SDE case the martingale has an explicit…