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Confidence intervals centred on bootstrap smoothed estimators: an impossibility result

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  • Paul Kabaila

    (La Trobe University)

  • Christeen Wijethunga

    (La Trobe University)

Abstract

Frequentist confidence intervals that include some element of data-based model selection or model averaging is an active area of research. Assessments of the performance, in terms of coverage and expected length, of such intervals yield few positive results. Efron, JASA 2014, proposed a confidence interval centred on a bootstrap smoothed estimator, with width proportional to an estimator of Efron’s delta method approximation to the standard deviation of this estimator. Recently, Kabaila and Wijethunga assessed the performance of this confidence interval using a testbed consisting of two nested linear regression models, with error variance assumed known. This interval was shown to have far better coverage properties than the corresponding post-model-selection confidence interval. However, its expected length properties were not as good as had been hoped for. For this testbed, we ask the following question. Does there exist a formula for the data-based width of a confidence interval centred on the bootstrap smoothed estimator so that it has good performance in terms of both coverage and expected length? Using a decision-theoretic performance bound we answer this question in the negative.

Suggested Citation

  • Paul Kabaila & Christeen Wijethunga, 2024. "Confidence intervals centred on bootstrap smoothed estimators: an impossibility result," Statistical Papers, Springer, vol. 65(3), pages 1531-1551, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01454-9
    DOI: 10.1007/s00362-023-01454-9
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    References listed on IDEAS

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    1. Paul Kabaila & A. H. Welsh & Waruni Abeysekera, 2016. "Model-Averaged Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 35-48, March.
    2. Turek, Daniel & Fletcher, David, 2012. "Model-averaged Wald confidence intervals," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2809-2815.
    3. Paul Kabaila, 2009. "The Coverage Properties of Confidence Regions After Model Selection," International Statistical Review, International Statistical Institute, vol. 77(3), pages 405-414, December.
    4. Bradley Efron, 2014. "Estimation and Accuracy After Model Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 991-1007, September.
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