## Admissible and optimal confidence bands in linear regression |

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1-a bands band forms band on B,B band over B,B Bohrer Bowden bands central section Chapter CJl;B CJL.g CJL.jj class of band class of forms coefficient Comparisons concept considered continuous function contrapositive convex set Cornell University corresponding criterion CX;B decision theory defined derived design points discontinuous band discrete-valued dominates equivalent exact Example experimenter Figure Fix B>0 fixed-width band fixed-width form formulation Gafarian gives Graybill-Bowden Hence Hoel hyperbolic bands hyperbolic form implies inadmissible infinite strips interest interior diagonal intermediate value theorem intersecting interval Jl(B Jl(t kJl(B kJl(t Lemma lim t|B Jl'(t linear segment bands maximize maximum minimal complete class minimax Naiman non-decreasing notation Notice numerical quadrature optimal design parabolic piecewise polynomial regression PQ(t predictor variable probability constraint problem Proceed by contradiction Proof restricted convex form result simple linear slope solution set symmetric band Theorem tion weight function Working-Hotelling hyperbola Wynn and Bloomfield x-optimal