This is an advanced topics course on time series analysis and high-dimensional statistics. It will provide a systematic introduction to two research topics: selfnormalization (SN) for time series inference and nonlinear dependence metrics and their statistical applications.
For self-normalization, we plan to cover its use for both confidence interval construction and hypothesis testing in the setting of stationary multivariate time series, functional time series, and high-dimensional time series. Change-point testing and estimation based on self-normalization will be introduced in detail for both low and high-dimensional data. Some recent work which combines sample splitting and self-normalization will also be presented. The course assumes that the student has the basic background of time series analysis and some research experience in time series analysis is desired but not a prerequisite.
For nonlinear dependence metrics, the emphasis will be placed on distance covariance, energy distance and their variants, including Hilbert-Schmidt Independence Criterion, maximum mean discrepancy, and martingale di?erence divergence, among others. The usefulness of these metrics will be demonstrated in some contemporary problems in statistics, such as dependence testing and variable screening/selection for high-dimensional data, as well as dimension reduction and diagnostic checking for multivariate time series. Some recent work on their applications to the inference of non-Euclidean data will also be discussed.
The presentations are based on the research results my collaborators and I have obtained in the past and will cover methodology, theory and practical data examples.
Course Attributes:
