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 nonlinear
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 Mainzer, R. and Kabaila, P. (2019)
<doi:10.32614/RJ-2019-026>, 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>.
