Small Area Estimation - Sampling Spatial Units for Agricultural Surveys - page 279

8
<

N d ʱ

1 if N d

N d
ʱ

ˉ d ¼ ; ð 11 : 25 Þ

otherwise

:

N d

where N d is the direct estimator of N d , and

is an arbitrary parameter for controlling
the contribution of the synthetic estimator. However, the common choice for this
parameter is

ʱ

:
The R instructions for this case are as follows.

ʱ ¼ 1

> domcomp < - ssd(dom ¼ coddom, sweight ¼ ws, domsize ¼ dsize,direct ¼
+ domdir[,c("coddom","yobs")], synthetic ¼ domsyn, data ¼ framesrs)
> domcomp

Domain ssd CompWeight

1 11 80.12641 1.0000000

2 12 93.37231 0.7758621

3 13 74.28390 1.0000000

4 21 98.02251 0.7407407

5 22 119.06890 0.9909910

6 23 96.89364 1.0000000

7 31 78.69029 1.0000000

8 32 96.72497 0.7758621

9 33 83.37624 1.0000000

The CompWeight are the weights attached to the direct estimators.
The indirect estimators (i.e., synthetic and composite) have the great benefit of
being simple to implement. These estimation techniques provide a more efficient
estimate than the corresponding design-based direct estimator for each SA, by using
implicit models that take advantage of the SAs. These models assume that all SAs
are similar with respect to the variable of interest, and do not consider the SA
specific variability. Unfortunately, if this assumption is violated, it can lead to
severe bias.
To overcome this limitation, an alternative estimation technique based on an
explicit linking model is provided in the next section. This approach provides a
better methodology for SAE by incorporating random area-specific effects, which
take into account the between area variations that are explained by auxiliary vari-
ables. In general, estimation methods based on an explicit model are more efficient
than traditional indirect methods based on an implicit model. This issue will be
discussed in the next section.