Page 354 - Contributed Paper Session (CPS) - Volume 7

CPS2125 Dian Handayani et al.

See Rao and Molina (2015) for further details of second-order approximation
and the estimator of MSE
to the Mean Square error (MSE) of
approximation.

3. EBP under Unit Level Lognormal Model:
Berg and Chandra (2014) developed Empirical Best Prediction (EBP)
method to estimate linear parameter, i.e. population mean, for variable of
interest have log normal distribution. The EBP is derived under unit level
lognormal model as follows:

2
2
where ~ (0, ), ~ (0, ) and and are
independent. Based on (5), is given by :

The EBP for population mean in small area- (denoted by ) is given by :

By properties of the normal distribution, for ∈ ̅,
(8)

By (7) and the moment generating function of the lognormal distribution, for
∈ ̅

By (9) and (7), the Best Predictor (BP) for is given by:

2
Since = (0, 1, , ) is usually unknown , the is replaced with to
2

obtain the Empirical Best Prediction (EBP) as follows :

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