A Cox-type regression model with change-points in the covariates |
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Authors: | Uwe Jensen Constanze Lütkebohmert |
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Affiliation: | 1.Institut für Angewandte Mathematik und Statistik,Universit?t Hohenheim,Stuttgart,Germany |
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Abstract: | We consider a Cox-type regression model with change-points in the covariates. A change-point specifies the unknown threshold at which the influence of a covariate shifts smoothly, i.e., the regression parameter may change over the range of a covariate and the underlying regression function is continuous but not differentiable. The model can be used to describe change-points in different covariates but also to model more than one change-point in a single covariate. Estimates of the change-points and of the regression parameters are derived and their properties are investigated. It is shown that not only the estimates of the regression parameters are [Formula: see text] -consistent but also the estimates of the change-points in contrast to the conjecture of other authors. Asymptotic normality is shown by using results developed for M-estimators. At the end of this paper we apply our model to an actuarial dataset, the PBC dataset of Fleming and Harrington (Counting processes and survival analysis, 1991) and to a dataset of electric motors. |
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Keywords: | Survival analysis Cox model Change-point Consistency Asymptotic normality |
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