Statistics 690D - Distribution-free Methods/Stat

In this class, we will discuss four methods that answer basic statistical questions without making distribution assumptions, and use properties such as exchangeability and invariance instead. Since these methods do not require specific models, they are often more robust and adaptable to complex data generating processes. The four methods we will cover are permutation test, bootstrap confidence interval, knockoffs selection and conformal prediction. They are widely used to compare distributions, construct confidence intervals, perform variable selections and compute prediction intervals. We will discuss principles and theory underlying these methods, as well as modern applications in real world settings. By the end of this class you will be able to articulate the theory of these methods, use them to standard problems, and formulate how to apply them in specific scenarios.

STATISTC 535 and 607 & 608 Prerequisites: STAT 607 and 608 or equivalent; familiarity with R programming language equivalent to STAT 535. We expect you to be familiar with the concept of confidence intervals, probability theory, convergence and central limit theorem.