Maximum modulus confidence bands

A family of confidence bands (simultaneous confidence regions) is given for EY = x′β that are piecewise-linear in x. Normality is assumed. These confidence bands are advocated over the usual hyperbolic band when the region of prime interest is distant from ${\overline{\bf x}}$ . In particular, this is the case when x?=?x(t) for time t and future time is of primary interest, that is for the prediction problem. For the case x′?=?(1, t), the family of bands includes that of Graybill and Bowden (J Am Stat Assoc 62:403–408, 1967).