## ciuupi: Confidence Intervals Utilizing Uncertain Prior Information

Computes a confidence interval for a specified linear combination of the
regression parameters in a linear regression model with iid normal errors
with known variance when there is uncertain prior information that a distinct
specified linear combination of the regression parameters takes a given
value. This confidence interval, found by numerical constrained
optimization, has the required minimum coverage and utilizes this uncertain
prior information through desirable expected length properties.
This confidence interval has the following three practical applications.
Firstly, if the error variance has been accurately estimated from previous
data then it may be treated as being effectively known. Secondly, for
sufficiently large (dimension of the response vector) minus (dimension of
regression parameter vector), greater than or equal to 30 (say),
if we replace the assumed known value of the error variance by its usual
estimator in the formula for the confidence interval then the resulting
interval has, to a very good approximation, the same coverage probability
and expected length properties as when the error variance is known. Thirdly,
some more complicated models can be approximated by the linear regression
model with error variance known when certain unknown parameters are replaced
by estimates. This confidence interval is described in Kabaila, P. and
Mainzer, R. (2017) <arXiv:1708.09543>, and is a member of the family of
confidence intervals proposed by Kabaila, P. and Giri, K. (2009)
<doi:10.1016/j.jspi.2009.03.018>.

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