Related papers: Threshold estimation for stochastic processes with…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…
We consider non-degenerate SDEs with a $\beta$-Holder continuous and bounded drift term and driven by a Levy noise $L$ which is of $\alpha$-stable type. If $\alpha \in [1,2)$ and $\beta \in (1 - \frac{\alpha}{2},1) $ we show pathwise…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
In the context of Independent Component Analysis (ICA), noisy mixtures pose a dilemma regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
This paper presents a new robust fault and state estimation based on recursive least square filter for linear stochastic systems with unknown disturbances. The novel elements of the algorithm are : a simple, easily implementable, square…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
Most physical data sets contain a stochastic contribution produced by measurement noise or other random sources along with the signal. Usually, neither the signal nor the noise are accurately known prior to the measurement so that both have…
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…
In this paper, we propose a sparse signal estimation algorithm that is suitable for many wireless communication systems, especially for the future millimeter wave and underwater communication systems. This algorithm is not only…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a…
This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian $\alpha$-stable L\'evy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for…
Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…
Estimating and detecting faults is crucial in ensuring safe and efficient automated systems. In the presence of disturbances, noise or varying system dynamics, such estimation is even more challenging. To address this challenge, this…
It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time…
We consider nonlinear filters for diffusion processes when the observation and signal noises are small and of the same order. As the noise intensities approach zero, the nonlinear filter can be approximated by a certain variational problem…