This was part of 
            Permutation and Causal Inference
          
        
            
      Permutation Inference under Dependence
                  
            EunYi Chung, University of Illinois at Urbana-Champaign
            
              Wednesday, August 23, 2023
            
          
              
    Abstract:  
    This paper studies permutation tests for dependent data. Under a weak dependence structure, we prove the asymptotic validity of block-wise permutation tests using studentization and the self- normalized test statistics, where the block size is not a function of the sample size. Monte Carlo simulation exercises confirm that both the studentized and the self- normalized block-wise permutation tests have the correct test sizes with moderate degrees of dependence.