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Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two…

Statistics Theory · Mathematics 2007-12-21 Ursula U. Müller , Anton Schick , Wolfgang Wefelmeyer

We present a simulation-based inference approach for two-stage estimators, focusing on extremum estimators in the second stage. We accommodate a broad range of first-stage estimators, including extremum estimators, high-dimensional…

Econometrics · Economics 2024-11-08 Aristide Houndetoungan , Abdoul Haki Maoude

Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…

Methodology · Statistics 2024-03-11 Cory W. Natoli , Edward D. White , Beau A. Nunnally , Alex J. Gutman , Raymond R. Hill

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…

Dynamical Systems · Mathematics 2022-11-17 Romeo Ortega , Alexey Bobtsov , Ramon Costa-Castello , Nikolay Nikolaev

Ergodic optimization is the study of extremal values of asymptotic dynamical quantities such as Birkhoff averages or Lyapunov exponents, and of the orbits or invariant measures that attain them. We discuss some results and problems.

Dynamical Systems · Mathematics 2018-04-24 Jairo Bochi

In this paper, a purely measurement-based method is proposed to estimate the dynamic system state matrix by applying the regression theorem of the multivariate Ornstein-Uhlenbeck process. The proposed method employs a recursive algorithm to…

Signal Processing · Electrical Eng. & Systems 2019-05-29 Hao Sheng , Xiaozhe Wang

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…

Statistics Theory · Mathematics 2011-11-10 Yury A. Kutoyants , Nakahiro Yoshida

A method for analyzing non-asymptotic guarantees of numerical discretizations of ergodic SDEs in Wasserstein-2 distance is presented by Sanz-Serna and Zygalakis in ``Wasserstein distance estimates for the distributions of numerical…

Machine Learning · Statistics 2024-12-03 Daniel Paulin , Peter A. Whalley

We propose a two stage procedure for the estimation of the parameters of a fairly general, continuous-time stochastic volatility. An important ingredient of the proposed method is the Cuchiero-Teichmann volatility estimator, which is based…

Statistics Theory · Mathematics 2018-12-31 Milan Merkle , Yuri F. Saporito , Rodrigo S. Targino

An Ornstein-Uhlenbeck (OU) process can be considered as a continuous time interpolation of the discrete time AR$(1)$ process. Departing from this fact, we analyse in this work the effect of iterating OU treated as a linear operator that…

Statistics Theory · Mathematics 2012-10-02 Argimiro Arratia , Alejandra Cabaña , Enrique M. Cabaña

This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with…

Machine Learning · Statistics 2022-09-16 Antoine Brochard , Bartłomiej Błaszczyszyn , Stéphane Mallat , Sixin Zhang

We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen, Hu, Wang…

Probability · Mathematics 2024-06-27 Fares Alazemi , Abdulaziz Alsenafi , Yong Chen , Hongjuan Zhou

The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two…

Data Analysis, Statistics and Probability · Physics 2015-05-14 Michael Wilkinson

We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced sophisticated…

Quantum Physics · Physics 2023-09-14 Daniel K. Mark , Joonhee Choi , Adam L. Shaw , Manuel Endres , Soonwon Choi

We present results on parameter estimation and non-parameter estimation of the linear partially observed Gaussian system of stochastic differential equations. We propose new one-step estimators which have the same asymptotic properties as…

Statistics Theory · Mathematics 2019-04-23 Yury A. Kutoyants , Li Zhou

We consider the class of all stationary Gaussian process with explicit parametric spectral density. Under some conditions on the autocovariance function, we defined a GMM estimator that satisfies consistency and asymptotic normality, using…

Statistics Theory · Mathematics 2017-01-18 Luis A. Barboza , Frederi G. Viens

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

Methodology · Statistics 2014-10-29 Nicolas Brunel , Quentin Clairon

We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…

Statistics Theory · Mathematics 2023-07-10 Alexandre Lecestre

We consider a model describing a neuron and the input it receives from its dendritic tree when this input is a random perturbation of a periodic deterministic signal, driven by an Ornstein-Uhlenbeck process. The neuron itself is modeled by…

Probability · Mathematics 2014-09-19 R. Höpfner , E. Löcherbach , M. Thieullen

We propose estimators for the parameters of the Linnik L$(\alpha,\gamma)$ distribution. The estimators are derived from the moments of the log-transformed Linnik distributed random variable, and are shown to be asymptotically unbiased. The…

Methodology · Statistics 2017-03-27 Dexter Cahoy