Permutation Test in Dependent Data

Slide

Permutation tests are powerful nonparametric tools for assessing statistical significance without relying on distributional assumptions. They are widely used in various domains, especially when the null distribution of a test statistic is unknown or difficult to derive analytically. However, the classical permutation test relies critically on the “exchangeability” of data—an assumption often violated in dependent settings such as time series or spatial data. This talk focuses on adapting permutation testing to such dependent structures. I will first review the basic principle and typical applications of permutation tests under independence. Then, I will discuss methods designed to handle dependence, with particular emphasis on “block permutation” techniques that preserve local dependence while approximating exchangeability. Finally, I will introduce “studentization” approaches, as exemplified by recent developments in permutation testing for serial dependence in time series, which improve test validity and power by normalizing test statistics appropriately. Together, these strategies demonstrate how the permutation framework can be extended to rigorously address dependence while maintaining its intuitive and computational appeal.