The large sample coverage probability of confidence intervals in general regression models after a preliminary hypothesis test

Paul Kabaila and Rupert E. H. Kuveke

Scandinavian Journal of Statistics, 2019, vol. 46, issue 2, 432-445

Abstract: We derive a computationally convenient formula for the large sample coverage probability of a confidence interval for a scalar parameter of interest following a preliminary hypothesis test that a specified vector parameter takes a given value in a general regression model. Previously, this large sample coverage probability could only be estimated by simulation. Our formula only requires the evaluation, by numerical integration, of either a double or a triple integral, irrespective of the dimension of this specified vector parameter. We illustrate the application of this formula to a confidence interval for the odds ratio of myocardial infarction when the exposure is recent oral contraceptive use, following a preliminary test where two specified interactions in a logistic regression model are zero. For this real‐life data, we compare this large sample coverage probability with the actual coverage probability of this confidence interval, obtained by simulation.

Date: 2019
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https://doi.org/10.1111/sjos.12358

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Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:46:y:2019:i:2:p:432-445

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