Hybrid Resampling Confidence Intervals for Change-point or Stationary High-dimensional Stochastic Regression Models

Wei Dai The Chinese University of Hong Kong, Shenzhen Ka Wai Tsang The Chinese University of Hong Kong, Shenzhen

Statistics Theory and Methods´╝îData Analysis mathscidoc:2103.86001

Statistica Sinica, 2021
Herein, we use hybrid resampling to address (a) the long-standing problem of inference on change times and changed parameters in change-point ARX-GARCH models, and (b) the challenging problem of valid confidence intervals, after variable selection under sparsity assumptions, for the parameters in linear regression models with high-dimensional stochastic regressors and asymptotically stationary noise. For the latter problem, we introduce consistent estimators of the selected parameters and a resampling approach to overcome the inherent difficulties of post-selection confidence intervals. For the former problem, we use a sequential Monte Carlo for the latent states (representing the change times and changed parameters) of a hidden Markov model. Asymptotic efficiency theory and simulation and empirical studies demonstrate the advantages of the proposed methods.
change-point ARX-GARCH models, coverage probability of credible and confidence intervals, double block bootstrap, hidden Markov
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@inproceedings{wei2021hybrid,
  title={Hybrid Resampling Confidence Intervals for Change-point or Stationary High-dimensional Stochastic Regression Models },
  author={Wei Dai, and Ka Wai Tsang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210304221515907722736},
  booktitle={Statistica Sinica},
  year={2021},
}
Wei Dai, and Ka Wai Tsang. Hybrid Resampling Confidence Intervals for Change-point or Stationary High-dimensional Stochastic Regression Models . 2021. In Statistica Sinica. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210304221515907722736.
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