Probability and Statistics
Statistical methodsoffer a powerful toolkit to extract useful information from massive and noisy observational data. This course introduces studentstomodern statistical methods and their theoretical foundations in high-dimensional and nonparametric models. In this course, we will covermodern statistical methods developed over the past 20 years, analyzetheir asymptotic properties and probabilistic foundations, and show how these methods can be applied into real data applications. Selected topicsinclude:high-dimensional and nonparametric estimation, minimax lower bound, multiple hypothesis testing, semiparametric models.