Wasserstein Bounds in the CLT of the MLE for the Drift Coefficient of a Stochastic Partial Differential Equation

Es-Sebaiy, Khalifa; Al-Foraih, Mishari

doi:10.3390/fractalfract5040187

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…Es-Sebaiy et al [28] obtained Berry-Esseen bound of the order O(K −3/2 ) for the MLE there by improving the bound O(K −1 ) of Kim and Park [45].…”

Section: Example 2 Heat Balance Equationmentioning

confidence: 97%

Quasi-likelihood and Quasi-Bayes Estimation in Noncommutative Fractional SPDEs

Bishwal

2024

Eur. J. Stat.

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We study the quasi-likelihood and quasi Bayes estimator of the drift parameter in the stochastic partial differential equations when the process is observed at the arrival times of a Poisson process. Unlike the previous work, no commutativity condition is assumed between the operators in the equation. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we plug-in this estimate in the quasi-likelihood to estimate the drift parameter. Under certain non-degeneracy assumptions on the operators, we obtain the consistency and the asymptotic normality of the estimators.

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“…Es-Sebaiy et al [28] obtained Berry-Esseen bound of the order O(K −3/2 ) for the MLE there by improving the bound O(K −1 ) of Kim and Park [45].…”

Section: Example 2 Heat Balance Equationmentioning

confidence: 97%

Quasi-likelihood and Quasi-Bayes Estimation in Noncommutative Fractional SPDEs

Bishwal

2024

Eur. J. Stat.

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“…For the fixed n and fixed parameter θ case, Es-Sebaiy et al [33] obtained Berry-Esseen bound of the order O(N −3/2 ) using the Stein-Malliavin theory for the MLE there by improving the bound O(N −1 ) of Kim and Park [39].…”

Section: 15)mentioning

confidence: 99%

Mixingale estimation function for mixed fractional SPDEs with random effect and random sampling

Bishwal¹

2022

Eur. J. Math. Appl.

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We study the mixingale estimation function estimator of the parameters in the fractional stochastic partial differential equation when the process is observed at the arrival times of a Poisson process with the presence of random effect. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we plug-in this estimate in the estimation function to estimate the drift parameter. We obtain the consistency and the asymptotic normality of the mixingale estimation function estimator.

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Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency

Es-Sebaiy

Al-Foraih

2023

J Inequal Appl

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This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted θ, for the Ornstein-Uhlenbeck process $X := \{X_{t},t\geq 0\}$ X : = { X t , t ≥ 0 } observed at high frequency. We provide an approximate minimum contrast estimator and an approximate maximum likelihood estimator of θ, namely $\widetilde{\theta}_{n}:= {1}/{ (\frac{2}{n} \sum_{i=1}^{n}X_{t_{i}}^{2} )}$ θ ˜ n : = 1 / ( 2 n ∑ i = 1 n X t i 2 ) , and $\widehat{\theta}_{n}:= -{\sum_{i=1}^{n} X_{t_{i-1}} (X_{t_{i}}-X_{t_{i-1}} )}/{ (\Delta _{n} \sum_{i=1}^{n} X_{t_{i-1}}^{2} )}$ θ ˆ n : = − ∑ i = 1 n X t i − 1 ( X t i − X t i − 1 ) / ( Δ n ∑ i = 1 n X t i − 1 2 ) , respectively, where $t_{i} = i \Delta _{n}$ t i = i Δ n , $i=0,1,\ldots , n $ i = 0 , 1 , … , n , $\Delta _{n}\rightarrow 0$ Δ n → 0 . We provide Wasserstein bounds in the central limit theorem for $\widetilde{\theta}_{n}$ θ ˜ n and $\widehat{\theta}_{n}$ θ ˆ n .

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Wasserstein Bounds in the CLT of the MLE for the Drift Coefficient of a Stochastic Partial Differential Equation

Cited by 3 publications

References 15 publications

Quasi-likelihood and Quasi-Bayes Estimation in Noncommutative Fractional SPDEs

Quasi-likelihood and Quasi-Bayes Estimation in Noncommutative Fractional SPDEs

Mixingale estimation function for mixed fractional SPDEs with random effect and random sampling

Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency

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