The name is absent

23

As shown above, Ao(t) cancels in the numerator and denominator. We extended
the Cox partial likelihood function in Section 3.3.3.

2.3.5 Breslow’s method

Breslow’s method can be used to estimate the baseline cumulative hazard function.

The Breslow’s estimator is given by

ʌo(θ = ∑o⅛) ⁼ Σ V-                  (²'¹⁸)

t_i<t         ^ti<^t.⅛

This method is further utilized in Chapter 3 Equations 3.13 and 3.14.

2.4 Introduction to copulas

Copulas are “multivariate distribution functions whose one-dimensional margins are
uniform on the interval (0,1)” (Nelsen 2006). Copulas are frequently utilized to model
the dependent structure among variables, and have broad applications in survival
analysis and actuarial science. Especially since Li (2000) first introduced copulas into
the modeling of default risks, researchers in the finance field have shown increasing
interest in applying copulas to address extensive financial topics.

Basically, copulas provide a convenient way to model two or more dependent
variables in terms that it does not require knowing explicitly either the function form
of the variables’ joint distribution or their marginal distributions. For any continuous
variable, the cumulative distribution function follows a uniform distribution, thus

<<   33   34   35   36   37   38   39   >>

More intriguing information