Estimation of split-points in binary regression

Abstract Let Y = m ( X )+ ϵ be a regression model with a dichotomous output Y and a step function m with exact one jump at a point θ and two different levels a and b . In the applied sciences the parameter θ is interpreted as a split-point whereas b and 1- a are known as positive and negative predictive value, respectively. We prove n -consistency and a weak convergence type result for a two-step plug-in maximum likelihood estimator of θ . The limit variable is not normal, but a maximizing point of a compound Poisson process on the real line. Estimation of ( a,b ) yields the usual √ n -consistency with normal limit. Both results can be extended to a multivariate weak limit theorem. It allows for the construction of asymptotic confidence intervals for ( θ , a,b ). The theory is applied to real life data of a large epidemiological study.