Test and confidence set for the difference of the x-coordinates of the vertices of two quadratic regression models

摘要

In this article, an exact test and a confidence set for the difference of thex-coordinates of the vertices of quadratic regression models is derived. It is assumed that the quadratic coefficients of both parabolae are equal, so the mentioned difference can equally be related to those x-coordinates where the parabolae have definite given gradient. The limits of the confidence set are given by mathematical formulae. They are implemented in Fortran programs that can be downloaded from the web. The confidence set need not be an interval. This is shown by an example based on nitrogen-rate trials in Germany, where the wheat yields are modeled as quadratic functions of the nitrogen input.