An exact confidence band for one-dimensional polynomial regression

Abstract

An exact piecewise polynomial simultaneous confidence band is described for one-dimensional ( p —1)th order polynomial regression. The band is constructed by placing intervals around the estimated response at the zeros of the p th order orthogonal polynomial with respect to the design points. Since under the usual assumptions the response estimates are uncorrelated at these zeros, the construction of the exact band in the normal case is made easy.