Maximum modulus confidence bands

A family of confidence bands (simultaneous confidence regions) is given for EY=<Emphasis Type="Bold">x′<Emphasis Type="BoldItalic">β that are piecewise-linear in <Emphasis Type="Bold">x. Normality is assumed. These confidence bands are advocated over the usual hyperbolic band when the region of prime interest is distant from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\overline{\bf x}}$$</EquationSource> </InlineEquation>. In particular, this is the case when <Emphasis Type="Bold">x = <Emphasis Type="Bold">x(t) for time t and future time is of primary interest, that is for the prediction problem. For the case <Emphasis Type="Bold">x′ = (1, t), the family of bands includes that of Graybill and Bowden (J Am Stat Assoc 62:403–408, <CitationRef CitationID="CR5">1967</CitationRef>). Copyright Springer-Verlag 2012