Rates of weak convergence of approximate minimum contrast estimators for the discretely observed Ornstein–Uhlenbeck process

Bishwal, Jaya P. N.

doi:10.1016/j.spl.2006.02.010

Cited by 12 publications

(3 citation statements)

References 8 publications

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“…Lemma 2.1 (a) is from Bishwal [2] and proof of (b) is elementary. Proof of the following lemma is also elementary.…”

Section: Given a Positive Integer M Construct A Probability Mass Funmentioning

confidence: 98%

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Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling

Bishwal

2011

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The paper shows that the distribution of the normalized minimum contrast estimator of the drift parameter in the fractional Ornstein-Uhlenbeck process observed over [0, T ] converges to the standard normal distribution with an uniform error rate of the order O(T −1/2 ) for the case H > 1/2 where H is the Hurst exponent of the fractional Brownian motion driving the Ornstein-Uhlenbeck process. Then based on discrete observations, it introduces several approximate minimum contrast estimators and studies their rate of of weak convergence to normal distribution.MSC 2010 : Primary 62F12, 62M05; Secondary 60F05, 60H10

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“…Lemma 2.1 (a) is from Bishwal [2] and proof of (b) is elementary. Proof of the following lemma is also elementary.…”

Section: Given a Positive Integer M Construct A Probability Mass Funmentioning

confidence: 98%

“…where p j , j ∈ {1, 2, · · · , m} is a probability mass function of a discrete random variable S on 0 ≤ s 1 < s 2 …”

Section: Discrete Samplingmentioning

confidence: 99%

Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling

Bishwal

2011

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“…Note that the papers [2] and [4] provided explicit upper bounds for the Kolmogorov distance for the rates of convergence of the distribution of θ n and θ n , respectively. On the other hand, [7] provided Wasserstein bounds in central limit theorem for θ n .…”

Section: Introductionmentioning

confidence: 99%

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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Parameter Estimation in the Heston Model

Bishwal

2022

Parameter Estimation in Stochastic Volatility Models

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Rates of weak convergence of approximate minimum contrast estimators for the discretely observed Ornstein–Uhlenbeck process

Cited by 12 publications

References 8 publications

Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling

Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling

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

Parameter Estimation in the Heston Model

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