Page 353 - Contributed Paper Session (CPS) - Volume 7

CPS2125 Dian Handayani et al.
Handayani et al (2018) estimate the values of variable of interest for non-
sampled units using the expectation of the values of variable of interest. In this
paper, we extent the SEBP which provides the estimates of values of variable
of interest using conditional expectation the values of variable of interest
given the data and random area effects.

2. EBLUP under Nested Regression Mode:
In this section, we describe the EBLUP of population mean in small area
(denoted by ) under unit level model. Suppose there are small areas and
)
units within small area ( = 1,2 … ). The EBLUP of (denoted by
based on variable of interest and auxiliary information which are
available in units’ level is derived under nested error regression model as
follows:

= + + = 1,2 … ; = 1,2 … (1)
where is the parameter of fixed effect , is matrix of known positive
constant, is random area effect which is assumed to be independently
normally distributed ~ (0, 2) and is sampling error unit- in small
area which is also assumed to be independently normally distributed

2
~ (0, )
The estimation of will be based on the selected sample with size is , =
1,2 … . The mean
of the in small area can be written by :

+ ∑∈ ] ; = 1,2 … (2)

where denotes sampled observations and non-sampled observations.
Under model (1) for small area , the best linear unbiased predictor (BLUP) for
is given by :

(3)

is a shrinkage factor where (ratio between the model variance relative to
̂

−1
the total variance); = ( −1 ) ( −1 ) is a weighted least squares
estimator of , ̅ and ̅ are the sample means of the interested variable

and auxiliary variable in small area i (Rao and Molina, 2015).
2
2
In practice, the parameters and are usually unknown. By replacing
2
2
2
2
( , ) in (3) by their estimates ( , ), the empirical best linear unbiased
predictor (EBLUP) of is obtained:
340 | I S I W S C 2 0 1 9