14
Definition 1. The indicator function of a set A, most often denoted by Ia(x), is the
function
{1 , x ∈ A,
0 , x ¢. A.
An alternative notation is I(x ∈ A}.
In Section 3.3.3 we explain how the proposed method has a different indicator
function than the traditional definition.
2.2.2 Likelihood function
A likelihood function is defined as in Casela and Berger (2002):
Definition 2. Let f(x∖θ) denote the joint probability density function of the sample
X = (Λ"ι, ...,Λra). Then, given that X = x is observed, the function of θ defined by
L(θ∖x) = f(x∖θ) (2.1)
is called the likelihood function.
In this research, we maximize the extended partial likelihood function to get the
optimal parameter estimators.
2.2.3 Bootstrapping method
Bootstrapping is a re-sampling technique. We retake samples from the original sam-
ple with replacement while following an approximating distribution. One standard
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