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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

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality…

Statistics Theory · Mathematics 2023-03-23 Koulik Khamaru , Yash Deshpande , Tor Lattimore , Lester Mackey , Martin J. Wainwright

In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…

Statistics Theory · Mathematics 2021-10-07 Karine Bertin , Soledad Torres , Lauri Viitasaari

Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes…

Computation · Statistics 2015-07-15 Muhammad Farooq , Ingo Steinwart

In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS)…

Systems and Control · Electrical Eng. & Systems 2023-09-07 Xinghua Zhu , Zhixin Liu

Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…

Statistics Theory · Mathematics 2024-12-24 Alessandro De Gregorio , Dario Frisardi , Francesco Iafrate , Stefano Iacus

In this paper, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is…

Systems and Control · Electrical Eng. & Systems 2022-12-19 Siyu Xie , Yaqi Zhang , Lei Guo

The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…

Statistics Theory · Mathematics 2008-06-19 Ouerdia Arkoun , Serguei Pergamenchtchikov

We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…

Probability · Mathematics 2018-02-06 Panpan Ren , Jiang-Lun Wu

In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…

Statistics Theory · Mathematics 2025-04-16 Mika Meitz , Alexander Shapiro

This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been…

Probability · Mathematics 2019-09-17 Zhaobo Liu , Chanying Li

The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…

Statistics Theory · Mathematics 2025-10-29 Iryna Dubovets'ka , Mykhailo Moklyachuk

We show that the posterior distribution of parameters in a hidden Markov model with parametric emission distributions and discrete and known state space is asymptotically normal. The main novelty of our proof is that it is based on a…

Statistics Theory · Mathematics 2021-06-01 Chunlei Wang , Sanvesh Srivastava

A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that data from a head-neck position tracking system, one of biomechanical models, show…

Methodology · Statistics 2024-02-13 Hojun You , Kyubaek Yoon , Wei-Ying Wu , Jongeun Choi , Chae Young Lim

We propose an adaptive randomized truncation estimator for Krylov subspace methods that optimizes the trade-off between the solution variance and the computational cost, while remaining unbiased. The estimator solves a constrained…

Numerical Analysis · Mathematics 2025-04-08 Qi Luo , Florian Schäfer

We formulate the notion of minimax estimation under storage or communication constraints, and prove an extension to Pinsker's theorem for nonparametric estimation over Sobolev ellipsoids. Placing limits on the number of bits used to encode…

Statistics Theory · Mathematics 2017-04-13 Yuancheng Zhu , John Lafferty

In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…

Statistics Theory · Mathematics 2020-11-16 Anuj Abhishek , Sakshi Arya

In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a…

Machine Learning · Statistics 2012-06-25 Stevenn Volant , Caroline Bérard , Marie-Laure Martin-Magniette , Stéphane Robin

In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp…

Statistics Theory · Mathematics 2020-05-15 Vlad Stefan Barbu , Slim Beltaief , Serguei Pergamenshchikov

Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…

Methodology · Statistics 2007-12-25 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc