What question did this study set out to answer?

To establish that subsampling constructs asymptotically valid confidence regions under minimal conditions without requiring uniform convergence to a limiting distribution.

December 1, 1994The Annals of StatisticsOpen Access

Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions

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Authors

DPDimitris N. PolitisHaliç University JRJoseph P. RomanoStanford University

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Implication

Theoretical analysis demonstrates asymptotically valid confidence regions via subsampling under minimal assumptions, indicating broad applicability across time series and random fields.

Key Points

To establish that subsampling constructs asymptotically valid confidence regions under minimal conditions without requiring uniform convergence to a limiting distribution.
Evaluated an approach that estimates the true sampling distribution by normalizing statistic values computed across smaller data subsamples.
Extended asymptotic validity proofs from independent and identically distributed data to stationary time series and homogeneous random fields.
Proved that the subsampling approach yields asymptotically valid confidence regions whenever a suitably normalized statistic possesses a limit distribution under the true model.
Demonstrated that the method eliminates the requirement of uniform convergence common to bootstrap procedures.
Showed practical applicability to estimating confidence intervals for spectral density functions in homogeneous random fields.

Cite This Study

Politis et al. (1994) studied this question.

synapsesocial.com/papers/6a0ea6b825c30b2cc7f9a4da https://doi.org/10.1214/aos/1176325770

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Implication

Theoretical analysis demonstrates asymptotically valid confidence regions via subsampling under minimal assumptions, indicating broad applicability across time series and random fields.

Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions

Discussion

Member takes

Implication

Key Points

Cite This Study

Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions

Discussion

Member takes

Implication

Key Points

Cite This Study

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