Moderate Deviations for Drift Parameter Estimations in Reflected Ornstein–Uhlenbeck Process

For an Ornstein–Uhlenbeck process driven by fractional Brownian motion with Hurst index [Formula: see text], we show the Berry–Esséen bound of the least squares estimator of the drift parameter based on the continuous-time observation. We use an approach based on Malliavin calculus given by Kim and Park [Optimal Berry–Esséen bound for statistical estimations and its application to SPDE, J. Multivariate Anal. 155 (2017) 284–304].

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Speed of Convergence of the Maximum Likelihood Estimator in the Ornstein-Uhlenbeck Process

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319950310 ◽

1995 ◽

Vol 45 (3-4) ◽

pp. 245-252 ◽

Cited By ~ 5

Author(s):

J. P. N. Bishwal ◽

Arup Bose

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Subject Classification ◽

Speed Of Convergence ◽

Primary 62F12 ◽

Likelihood Estimator ◽

Uhlenbeck Process ◽

Ornstein Uhlenbeck Process ◽

Drift Parameter

Berry-Bsseen bounds with random norming and Jario deviation probabilities arc derived for the maximum likelihood estimator of the drift parameter in tho Ornstoin-Uhlenbeck proccss. AMS (1991) Subject Classification: Primary 62F12, 62M05 Secondary 60FOS, 60F10

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Hypothesis testing of the drift parameter sign for fractional Ornstein–Uhlenbeck process

Electronic Journal of Statistics ◽

10.1214/17-ejs1237 ◽

2017 ◽

Vol 11 (1) ◽

pp. 385-400 ◽

Cited By ~ 10

Author(s):

Alexander Kukush ◽

Yuliya Mishura ◽

Kostiantyn Ralchenko

Keyword(s):

Hypothesis Testing ◽

Uhlenbeck Process ◽

Ornstein Uhlenbeck Process ◽

Drift Parameter

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Self-normalized asymptotic properties for the parameter estimation in fractional Ornstein–Uhlenbeck process

Stochastics and Dynamics ◽

10.1142/s0219493719500187 ◽

2019 ◽

Vol 19 (03) ◽

pp. 1950018 ◽

Cited By ~ 2

Author(s):

Hui Jiang ◽

Junfeng Liu ◽

Shaochen Wang

Keyword(s):

Large Deviations ◽

Asymptotic Properties ◽

Moderate Deviations ◽

Delta Method ◽

Fourth Moment ◽

Test Statistics ◽

Uhlenbeck Process ◽

Ornstein Uhlenbeck Process ◽

Deviation Inequalities ◽

Type Ii Errors

In this paper, we consider the self-normalized asymptotic properties of the parameter estimators in the fractional Ornstein–Uhlenbeck process. The deviation inequalities, Cramér-type moderate deviations and Berry–Esseen bounds are obtained. The main methods include the deviation inequalities and moderate deviations for multiple Wiener–Itô integrals [P. Major, Tail behavior of multiple integrals and U-statistics, Probab. Surv. 2 (2005) 448–505; On a multivariate version of Bernsteins inequality, Electron. J. Probab. 12 (2007) 966–988; M. Schulte and C. Thäle, Cumulants on Wiener chaos: Moderate deviations and the fourth moment theorem, J. Funct. Anal. 270 (2016) 2223–2248], as well as the Delta methods in large deviations [F. Q. Gao and X. Q. Zhao, Delta method in large deviations and moderate deviations for estimators, Ann. Statist. 39 (2011) 1211–1240]. For applications, we propose two test statistics which can be used to construct confidence intervals and rejection regions in the hypothesis testing for the drift coefficient. It is shown that the Type II errors tend to be zero exponential when using the proposed test statistics.

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Berry-Esseen bounds and ASCLTs for drift parameter estimator of mixed fractional Ornstein-Uhlenbeck process with discrete observations

Теория вероятностей и ее применения ◽

10.4213/tvp5238 ◽

2019 ◽

Vol 64 (3) ◽

pp. 502-525

Author(s):

Farez Alazemi ◽

Soukhana Douissi ◽

Khalifa Es-Sebaiy ◽

...

Keyword(s):

Discrete Observations ◽

Parameter Estimator ◽

Uhlenbeck Process ◽

Ornstein Uhlenbeck Process ◽

Drift Parameter

Рассматривается задача оценивания сноса смешанного процесса Орнштейна-Уленбека на основе наблюдений в фиксированные дискретные моменты времени. С использованием исчисления Маллявена и недавнего анализа Нурдина-Пеккати исследуется асимптотическое поведение оценки. Более точно, изучаются сильная состоятельность и асимптотическое распределение оценки; установлена также скорость ее сходимости по распределению для всех $H\in(0,1)$. Более того, доказано, что в случае $H\in(0,3/4]$ оценка удовлетворяет центральной предельной теореме для сходимости почти наверное.

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CONTROLLED DRIFT ESTIMATION IN FRACTIONAL DIFFUSION LINEAR SYSTEMS

Stochastics and Dynamics ◽

10.1142/s0219493712500256 ◽

2013 ◽

Vol 13 (03) ◽

pp. 1250025 ◽

Cited By ~ 1

Author(s):

ALEXANDRE BROUSTE ◽

CHUNHAO CAI

Keyword(s):

Maximum Likelihood ◽

Laplace Transform ◽

Fractional Diffusion ◽

Likelihood Estimator ◽

Uhlenbeck Process ◽

Drift Estimation ◽

Partially Observed ◽

Ornstein Uhlenbeck Process ◽

Drift Parameter

This paper is devoted to the determination of the asymptotical optimal input for the estimation of the drift parameter in a partially observed but controlled fractional Ornstein–Uhlenbeck process. Large sample asymptotical properties of the Maximum Likelihood Estimator are deduced using Ibragimov–Khasminskii program and Laplace transform computations.

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Cramér-type moderate deviations for the likelihood ratio process of Ornstein–Uhlenbeck process with shift

Stochastics and Dynamics ◽

10.1142/s0219493721500271 ◽

2020 ◽

Vol 21 (02) ◽

pp. 2150027

Author(s):

Hui Jiang ◽

Hui Liu

Keyword(s):

Likelihood Ratio ◽

Decay Rates ◽

Moderate Deviations ◽

Uhlenbeck Process ◽

Testing Problem ◽

Analysis Techniques ◽

Log Likelihood ◽

Ornstein Uhlenbeck Process ◽

Deviation Inequalities ◽

Error Probabilities

For the Ornstein–Uhlenbeck process in stationary and explosive cases, this paper studies Cramér-type moderate deviations for the log-likelihood ratio process. As an application, we give the negative regions of drift testing problem, and also obtain the decay rates of the error probabilities. The main methods of this paper consist of mod-[Formula: see text] convergence approach, deviation inequalities for multiple Wiener–Itô integrals and asymptotic analysis techniques.

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