随机抽样下预平均Hayashi-Yoshida估计的极限定理
Limit theorems for the pre-averaged Hayashi-Yoshida estimator with random sampling
摘要：
我们将着重于估计两个扩散过程中观察到的非同步方式的综合协方差。观测数据被一些噪声污染，这些噪声可能与扩散过程的返回相关，而采样时间也可能取决于所观测的过程。在高频情形下，我们考虑了预平均Hayashi-Yoshida估计的一个修正形式，证明了这类估计具有相合性和渐近混合正态性，并获得了最优的收敛速率.
英文摘要：
We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which is possibly correlated with the returns of the diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi-Yoshida estimator, and we show that such a kind of estimators has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
