论文标题
在高频下观察到的Ornstein-uhlenbeck过程的近似MCE和MLE的CLT中的Wasserstein边界
Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency
论文作者
论文摘要
本文介绍了漂移系数的估计器中心限制定理的收敛速率，表示为$θ$，对于Ornstein-Uhlenbeck过程$ x \ coloneqq \ {x_t，x_t，t \ geq0 \} $以高频的高频观察到。我们提供了近似最小对比度估计器和$θ$的近似最大似然估计器，即$ \widetildeθ_{n} \ coloneqq {1}/{\ left（\ frac {2} {n} {n} {n} \ sum_ {i = 1}^{n} x_ {t_ {i}}}^{2} {2} \ right）} $， 和$ \widehatθ_{n} \ coloneqq- {\ sum_ {i = 1}^{n} x_ {t_ {i-1}}} \ left（x_ {x_ {t_ {i}}} - x_ \ sum_ {i = 1}^{n} x_ {t_ {t_ {i-1}}}^{2} {2} \ right）} $，其中$ t_ {i} =iΔ__{n} $， $ i = 0,1，\ ldots，n $，$δ_{n} \ rightarrow 0 $。 我们在 $ \widetildeθ_{n} $和$ \wideHatθ_{n} $的中央限制定理。
This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted $θ$, for a Ornstein-Uhlenbeck process $X \coloneqq \{X_t,t\geq0\}$ observed at high frequency. We provide an Approximate minimum contrast estimator and an approximate maximum likelihood estimator of $θ$, namely $\widetildeθ_{n}\coloneqq {1}/{\left(\frac{2}{n} \sum_{i=1}^{n}X_{t_{i}}^{2}\right)}$, and $\widehatθ_{n}\coloneqq -{\sum_{i=1}^{n} X_{t_{i-1}}\left(X_{t_{i}}-X_{t_{i-1}}\right)}/{\left(Δ_{n} \sum_{i=1}^{n} X_{t_{i-1}}^{2}\right)}$, respectively, where $ t_{i} = i Δ_{n}$, $ i=0,1,\ldots, n $, $Δ_{n}\rightarrow 0$. We provide Wasserstein bounds in central limit theorem for $\widetildeθ_{n}$ and $\widehatθ_{n}$.
