摘要翻译：
考虑了基于高频观测的高维扩散过程的积分协方差矩阵的估计。我们从研究最常用的估计量，实现协方差(RCV)矩阵开始。结果表明，在高维情形下，当维数$P$和观测频率$N$以相同的速率增长时，RCV的极限谱分布(LSD)不仅取决于目标ICV的协波动过程，而且还取决于协波动过程随时间的变化。我们建立了加权样本协方差矩阵的一个Mar\v{c}Enko-Pastur型定理，在此基础上我们得到了一类扩散过程的RCV的一个Mar\v{c}Enko-Pastur型定理。结果明确地说明了协波动过程的时变性如何影响RCV的LSD。我们进一步提出了一种替代估计，即时变调整的实现协方差(TVARCV)矩阵。我们通过MAR\V{C}Enko-Pastur方程证明，对于$\Mathcal{C}$类的过程，TVARCV具有LSD完全依赖于目标ICV的LSD这一理想性质，因此，TVARCV可以利用现有的算法来恢复ICV的经验谱分布。
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英文标题：
《On the estimation of integrated covariance matrices of high dimensional
  diffusion processes》
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作者：
Xinghua Zheng, Yingying Li
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最新提交年份：
2012
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We show that in the high dimensional case when the dimension $p$ and the observation frequency $n$ grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process not only through the targeting ICV, but also on how the covolatility process varies in time. We establish a Mar\v{c}enko--Pastur type theorem for weighted sample covariance matrices, based on which we obtain a Mar\v{c}enko--Pastur type theorem for RCV for a class $\mathcal{C}$ of diffusion processes. The results explicitly demonstrate how the time variability of the covolatility process affects the LSD of RCV. We further propose an alternative estimator, the time-variation adjusted realized covariance (TVARCV) matrix. We show that for processes in class $\mathcal {C}$, the TVARCV possesses the desirable property that its LSD depends solely on that of the targeting ICV through the Mar\v{c}enko--Pastur equation, and hence, in particular, the TVARCV can be used to recover the empirical spectral distribution of the ICV by using existing algorithms.
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PDF链接：
https://arxiv.org/pdf/1005.1862