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Estimation of split-points in binary regression

Author

Listed:
  • Ferger Dietmar
  • Klotsche Jens

    (Technische Universität Dresden, Institue of Clinical Psychology and Psychotherapy, Dresden, Deutschland)

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.

Suggested Citation

  • Ferger Dietmar & Klotsche Jens, 2009. "Estimation of split-points in binary regression," Statistics & Risk Modeling, De Gruyter, vol. 27(02), pages 93-128, December.
    • Handle: RePEc:bpj:strimo:v:27:y:2009:i:2:p:93-128:n:2
    DOI: 10.1524/stnd.2009.1023
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    References listed on IDEAS

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    1. Dietmar Ferger, 2004. "A continuous mapping theorem for the argmax‐functional in the non‐unique case," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 83-96, February.
    2. Astrid Dempfle & Winfried Stute, 2002. "Nonparametric estimation of a discontinuity in regression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 233-242, May.
    3. Koul, Hira L. & Qian, Lianfen & Surgailis, Donatas, 2003. "Asymptotics of M-estimators in two-phase linear regression models," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 123-154, January.
    4. Müller, Hans-Georg & Song, Kai-Sheng, 1997. "Two-stage change-point estimators in smooth regression models," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 323-335, June.
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