The name is absent

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, ...,Λ_ra). 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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