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3.6. Simultaneous Confidence Intervals

If H0: LB = 0 is rejected, it may be of interest to provide the confidence intervals for the individual components of LB (or B if L= Ik+1) or the linear functions of these components. Under the assumption of the full rank of X, a set of simultaneous confidence intervals for the linear combinations of the type cLBd corresponding to the linear hypothesis H0: LB = 0 can be constructed.

Noting that H0(c,d) : (cLBd=0 is true for all c and d if and only if H0 is true, we can write H0 as the intersection of all such H0(c,d) : (cLBd=0. Testing of H0(c,d) : cLBd=0 can be done using the appropriate F test. Let the corresponding F statistic be F(c,d) and let Fα be the cutoff point. Then, H0 is not rejected if ...

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