Agriculture Reference
In-Depth Information
appear to be appropriate. In this situation, the direct survey estimates are the sum of
a model of the true population values (i.e., the above state-space time series models)
and a model for the sampling errors.
At the end of each year, the monthly model-based estimates (i.e., SAE estimates)
are modified so that their annual mean is equal to the corresponding mean of the
direct CPS estimates. Obviously, in this way, the aim of the benchmarking is to
protect against misspecification of the model.
One benchmarking method that
is often used in practical applications is
(Pfeffermann 2013 )
0
1
X
D
g j ʸ j , design
@
A
j ¼1
ʸ
ʸ d , model :
bench
d , 1
¼
ð 11
:
49 Þ
X
D
g j ʸ j , model
j ¼1
This approach is called the ratio or pro-rata adjustment.
Wang et al. ( 2008 ) derived the benchmarked BLUP (BBLUP) using the area
level model
d , model þ ʴ d X
D
ʸ d , BBLUP ¼ ʸ
ʸ j , design ʸ
BLUP
BLUP
j , model
g j
;
ð 11
:
50 Þ
j ¼1
! 1
X
D
j ¼1 ˆ 1
g j
ˆ 1
d
where ʴ d ¼
g d and ˆ d s are chosen positive weights. It is evident
j
2
˅
that the estimate of the variance
, on which depends the estimator in Eq. ( 11.49 ),
leads to the definition of the empirical BBLUP.
˃
Conclusions
In this chapter, we reviewed the problems and main methodologies of SAE,
with applications to artificial and agricultural data. It is well known that area-
specific sample data are not large enough for all SAs to provide adequately
precise estimates. We have described the direct, indirect, and model-based
approaches.
Each approach has advantages and disadvantages. For example, indirect
estimators can take advantage of data on related multiple characteristics
and/or auxiliary variables to produce better estimates at the SA level. Alter-
natively, model-based techniques can be appropriate, but they suffer from
validation problems.
(continued)
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