Statistical Problems in Large Volatility Matrix Estimation and Quantum Annealing Based Computing

随着现代“数据洪流”的增长，统计的重要性继续增加，统计方法的使用迅速发展。数据科学的新时代对传统的统计工具和计算技术提出了巨大的挑战;与此同时，数据洪流也为统计带来了前所未有的机遇。该项目计划通过创新的统计和计算方法来推进科学前沿的研究，以解决在处理大数据复杂问题时遇到的挑战。该项目对量子计算和高频金融的统计研究将解决实际问题，这些项目将创建先进有效的统计工具，直接应用于金融，量子计算和量子信息等领域。 该项目旨在对量子退火和关于高维矩阵的统计推断进行新的研究。这些目标需要开发统计方法，计算技术和理论，用于（i）应用于高频金融的大型扩散协方差矩阵的统计推断，以及（ii）量子计算和量子信息中量子退火的统计研究。该项目将开发严格支持的统计方法和计算技术，进一步加强这些重要主题的理论基础。

As the modern "data deluge" grows, the importance of statistics continues to increase, and uses of statistical methods rapidly evolve. The new era of data science poses great challenges to traditional statistical tools and computational techniques; yet, at the same time, the data deluge presents unprecedented opportunities to statistics. This project plans to advance research at the frontiers of science with innovative statistical and computational approaches that address the challenges encountered in handling complex problems with big data. The project's statistical research on quantum computing and high-frequency finance will address practical problems, and the projects will create advanced effective statistical tools with direct applications in fields including finance, quantum computation, and quantum information. This project seeks to conduct novel research on quantum annealing and statistical inference about large-dimensional matrices. The goals entail developing statistical methodologies, computing techniques, and theories for (i) statistical inference for large diffusion covariance matrices with applications to high-frequency finance, and (ii) statistical research on quantum annealing in quantum computation and quantum information. The project will develop rigorously-supported statistical methods and computational techniques, furthering the theoretical underpinning of these important topics.