Coverage bound for fixed-b subsampling and generalized subsampling for time series

Yinxiao Huang, Xiaofeng Shao

Research output: Contribution to journalArticlepeer-review


We investigate the upper bounds on coverage probabilities of the subsampling-based confidence sets in the time series setting. Under the fixed-b asymptotic framework, where b is the ratio of block size to sample size, we derive the limiting coverage bound, and obtain the finite sample coverage bound by simulations. Our findings suggest that the coverage bound is strictly below 1 for positive b, it can be far away from 1, and the fixed-b subsampling method in Shao and Politis (2013) can exhibit serious undercoverage when the dimension of the parameter is large, the time series dependence is (positively) strong, or b is large. To alleviate the problem, we propose a generalized subsampling method that combines useful features of fixed-b subsampling and self-normalization, and demonstrate its effectiveness in terms of delivering more accurate coverage via numerical studies.

Original languageEnglish (US)
Pages (from-to)1499-1524
Number of pages26
JournalStatistica Sinica
Issue number4
StatePublished - Oct 2016


  • Coverage bound
  • Pivot
  • Self-normalization
  • Subsampling

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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