Estimation of split-points in binary regression

Ferger Dietmar and Klotsche Jens
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Klotsche Jens: Technische Universität Dresden, Institue of Clinical Psychology and Psychotherapy, Dresden, Deutschland

Statistics & Risk Modeling, 2009, vol. 27, issue 02, 93-128

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.

Keywords: compound poisson process; M-estimation; regression with jump; rescaled marked empirical process; weak limit theorems (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1524/stnd.2009.1023

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