85
where λo(∙;?) is a baseline hazard function depending on an unknown parameter
7. This model is tested on many important distributions commonly used in survival
analysis, for instance, exponential, Weibull, extreme and log-logistic models for which
ʌo(^?) = 1; ty∙> e^it and C1 / (1 ÷72^71+1))j respectively.
Wu et al. (2003) provides a non-parametric estimator of the change-point in the
context of counting process, based upon a function of Nelson-Aalen type estimator.
The estimators for change-point and other parameters are shown to be consistent.
Monte Carlo simulation tests are conducted, which show that the proposed procedure
for estimating the change-point is effective.
Although independent censoring is considered in the proposed approach, the de-
pendent censoring is not included. Thus, the method can not be applied to this
dissertation directly.
5.2 Methodology
5.2.1 Models and parameter estimators
We are interested in testing the hypothesis on whether change-point(s) exist on the
copula-based hazard curve; and if so, how to locate it.
We consider the change-point model as below:
λ(f) =
λ0 exp(Z∙∕?)
λ1exp(Z-∕3)
0 ≤ t < θ,
t > θ.
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