Statistical theory and methods for high-dimensional data

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In modern statistical analysis, high-dimensional data are increasingly encountered in fields ranging from genetics and biology to engineering and finance. In genetics, microarray and next-generation sequencing technology can simultaneously measure expression levels of tens of thousands of genes in a single biological sample. In finance, the prices of hundreds of financial assets are observed at high-frequency and analyzed for portfolio allocation. However, the high dimensionality renders many classical multivariate statistics inappropriate or undefined. One of the primary reasons is that many multivariate statistics involve the sample covariance matrix, which is not a good estimate of its population counterpart in high-dimensional settings. In the next five to ten years, this research program will focus on developing novel statistical theory and methods in the following areas: test statistics and estimation procedures, which enjoy large-sample and high-dimension asymptotic properties, for high-dimensional mean vectors, covariance matrices and joint distributions. The development of this research program will have significant impact on everyday statistical analysis for high-dimensional data, and facilitate advances in a wide range of scientific investigations.