Construction Of A Conservative Confidence Region From Projections Of An Exact Confidence Region In Multiple Linear-Regression
Abbreviated Journal Title
BONFERRONI; SCHEFFE; WORKING-HOTELLING; Statistics & Probability
The problem of constructing a confidence region for simultaneously estimating p, p greater-than-or-equal-to 2, linear regression parameters for which confidence statements can be made on the individual parameters is revisited. Here, an intercept may be included among the p paremeters. The technique is due to Working and Hotelling (1929) and Scheffe (1959) and uses the p separate projections of the exact (1 - alpha) 100% confidence ellipsoid (ellipse if p = 2) to give confidence intervals for each regression parameter. The Cartesian product of these p confidence intervals gives a p-dimensional rectangle that contains the confidence ellipsoid and hence has a joint confidence coefficient of at least (1 - alpha). A simple calculus proof is given to determine these projections. The projection procedure is compared with the Bonferroni procedure for this case.
"Construction Of A Conservative Confidence Region From Projections Of An Exact Confidence Region In Multiple Linear-Regression" (1994). Faculty Bibliography 1990s. 1135.