Confidence intervals centred on bootstrap smoothed estimators: an impossibility result

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Statistical papers

سال: 2023

ISSN: ['2412-110X', '0250-9822']

DOI: https://doi.org/10.1007/s00362-023-01454-9