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We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…

Statistics Theory · Mathematics 2024-02-12 Maksym Luz , Mikhail Moklyachuk

We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…

Statistics Theory · Mathematics 2011-12-30 Marc Hoffmann , Axel Munk , Johannes Schmidt-Hieber

We study a new parametric approach for hidden discrete-time diffusion models. This method is based on contrast minimization and deconvolution and leads to estimate a large class of stochastic models with nonlinear drift and nonlinear…

Statistics Theory · Mathematics 2017-01-01 Salima El Kolei , Florian Pelgrin

We study Bayes procedures for the problem of nonparametric drift estimation for one-dimensional, ergodic diffusion models from discrete-time, low-frequency data. We give conditions for posterior consistency and verify these conditions for…

Statistics Theory · Mathematics 2013-02-01 Frank van der Meulen , Harry van Zanten

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…

Numerical Analysis · Mathematics 2018-04-10 Sebastian Krumscheid

We introduce a nonparametric spectral density estimator for continuous-time and continuous-space processes measured at fully irregular locations. Our estimator is constructed using a weighted nonuniform Fourier sum whose weights yield a…

Methodology · Statistics 2025-10-07 Christopher J. Geoga , Paul G. Beckman

We propose solution of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of a continuous time stochastic process with periodically correlated increments based on observations of…

Statistics Theory · Mathematics 2024-01-18 Maksym Luz , Mikhail Moklyachuk

We consider the question of estimating the drift and the invariant density for a large class of scalar ergodic diffusion processes, based on continuous observations, in $\sup$-norm loss. The unknown drift $b$ is supposed to belong to a…

Statistics Theory · Mathematics 2018-09-03 Cathrine Aeckerle-Willems , Claudia Strauch

Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…

Machine Learning · Statistics 2023-12-12 Yinuo Ren , Yiping Lu , Lexing Ying , Grant M. Rotskoff

The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…

Statistics Theory · Mathematics 2024-02-13 Oleksandr Masyutka , Mikhail Moklyachuk , Maria Sidei

Consider a diffusion process X, solution of a time-homogeneous stochastic differential equation. We assume that the diffusion process X is observed at discrete times, at high frequency, which means that the time step tends toward zero. In…

Statistics Theory · Mathematics 2025-06-23 Eddy Michel Ella Mintsa

We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…

Systems and Control · Electrical Eng. & Systems 2021-03-23 Christopher I. Calle , Shaunak D. Bopardikar

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…

Statistics Theory · Mathematics 2021-10-19 Oleksandr Masyutka , Mikhail Moklyachuk

We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…

Statistics Theory · Mathematics 2020-10-28 Shogo H Nakakita , Masayuki Uchida

We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the multivariate density of the finite dimensional distributions of which we aim to estimate. We assume that we observe the…

Statistics Theory · Mathematics 2014-07-08 Bert van Es , Peter Spreij

This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…

Numerical Analysis · Mathematics 2019-03-05 He Zhang , Xiantao Li , John Harlim

The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…

Statistics Theory · Mathematics 2021-10-18 Maksym Luz , Mikhail Moklyachuk

This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…

Statistics Theory · Mathematics 2024-06-27 Mikhail Moklyachuk

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…

Statistics Theory · Mathematics 2015-03-19 Markus Bibinger , Markus Reiß

We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…

Statistics Theory · Mathematics 2020-07-22 Shota Gugushvili , Frank van der Meulen , Moritz Schauer , Peter Spreij