vii
3.2.2 Which copula function to use?.................. 36
3.3 Methodology - extended Cox proportional hazards models...... 37
3.3.1 Event time and dependent censoring time models....... 37
3.3.2 Conditional survival probability functions ........... 39
3.3.3 Partial likelihood functions.................... 42
3.3.4 Iteration steps........................... 45
3.3.5 Remarks.............................. 50
3.4 Simulation study of dependent censoring................ 53
4 Application: How Does the 1999 Gramm-Leach-Bliley Act Impact
the Survival of Insurance Companies? 63
4.1 Basic framework ............................. 64
4.2 Data source and data structure..................... 65
4.3 How covariates are determined...................... 67
4.4 Sensitivity analysis and results...................... 69
5 A Change-Point Hazard Rate Model 81
5.1 Literature review............................. 82
5.1.1 The likelihood based approaches................. 82
5.1.2 Non-parametric approaches ................... 84
5.2 Methodology ............................... 85
5.2.1 Models and parameter estimators................ 85
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