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In this paper, we consider the robust adaptive non parametric estimation problem for the drift coefficient in diffusion processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed.…

Statistics Theory · Mathematics 2019-09-24 Evgeny Pchelintsev , Svyatoslav Perelevskiy , Irina Makarova

In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…

Optimization and Control · Mathematics 2013-12-19 J. C. Jimenez

We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…

Statistics Theory · Mathematics 2026-02-09 Emil S. Jørgensen , Michael Sørensen

This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…

Statistics Theory · Mathematics 2009-09-03 Yoichi Nishiyama

We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any…

Statistics Theory · Mathematics 2021-02-16 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…

Statistics Theory · Mathematics 2016-08-16 Jaime A. Londoño

We address the problem of parameter estimation for degenerate diffusion processes defined via the solution of Stochastic Differential Equations (SDEs) with diffusion matrix that is not full-rank. For this class of hypo-elliptic diffusions…

Statistics Theory · Mathematics 2024-09-04 Yuga Iguchi , Alexandros Beskos

We propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the…

Statistics Theory · Mathematics 2015-06-30 Yusuke Shimizu

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…

Statistics Theory · Mathematics 2015-12-29 Teppei Ogihara

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

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 finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…

Optimization and Control · Mathematics 2019-03-15 Melike Sirlanci , Susan E. Luczak , I. Gary Rosen

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…

Statistics Theory · Mathematics 2016-01-13 Aurore Delaigle , Peter Hall , Wen-Xin Zhou

This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with…

Statistics Theory · Mathematics 2026-03-17 Nicolas Marie

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

Machine Learning · Statistics 2026-04-01 Yuzhen Zhao , Yating Liu , Marc Hoffmann

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Statistics Theory · Mathematics 2017-12-05 Shogo H. Nakakita , Masayuki Uchida

In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In…

Methodology · Statistics 2023-12-18 Kenta Takatsu , Ted Westling

We consider a 1-dimensional diffusion process X with jumps. The particularity of this model relies in the jumps which are driven by a multidimensional Hawkes process denoted N. This article is dedicated to the study of a nonparametric…

Statistics Theory · Mathematics 2019-11-05 Charlotte Dion , Sarah Lemler

We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…

Statistics Theory · Mathematics 2009-09-29 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc

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