Estimates for the Points of Intersection of Two Polynomial Regressions

Let t* denote an unknown abscissa of intersection of two true regression functions μ1(t) and μ2(t). Under normality assumptions with no restraints on t* the maximum likelihood estimator of t* is shown to be the corresponding intersection of the sample regressions. When this estimate exists confidence intervals J can usually be obtained for t* by an application of the Student t-distribution. When t* is restrained to some known interval I, the ML estimate may or may not fall in I. A restrained ML estimate proposed is the limiting point of ∩I ∩J as the length of I ∩ J approaches zero. Confidence limits are obtained for the restrained estimate. Many practical difficulties are discussed.