ciuupi: An R package for Computing Confidence Intervals that Utilize Uncertain Prior Information

Abstract

We have created the R package ciuupi to compute confidence intervals that utilize uncertain prior information in linear regression. Unlike post-model-selection confidence intervals, the confidence interval that utilizes uncertain prior information (CIUUPI) implemented in this package has, to an excellent approximation, coverage probability throughout the parameter space that is very close to the desired minimum coverage probability. Furthermore, when the uncertain prior information is correct, the CIUUPI is, on average, shorter than the standard confidence interval constructed using the full linear regression model. In this paper we provide motivating examples of scenarios where the CIUUPI may be used. We then give a detailed description of this interval and the numerical constrained optimization method implemented in R to obtain it. Lastly, using a real data set as an illustrative example, we show how to use the functions in ciuupi.Y. L. Tseng and L. D. Brown. Good exact confidence sets for a multivariate normal mean.

Confidence intervals centred on bootstrap smoothed estimators

“…We know that the requirements that we have put forward are not excessively restrictive because, as shown by Kabaila & Giri (2009), Giri (2013) andMainzer &Kabaila (2019), it is possible to compute formulas for the centre and width of the confidence interval so that this interval has the attractive features (A1) and (A2), the desired minimum coverage probability 1 − α and scaled expected length that (a) has a maximum value that is not too much larger than 1 and (b) is substantially less than 1 when the simpler model is correct. Indeed, the R package ciuupi, described by Mainzer & Kabaila (2019), computes confidence intervals that have the attractive features (A1) and (A2), the desired minimum coverage probability 1 − α and for which the gain is set equal to the loss, where gain and loss are as defined in Section 6.…”