Agriculture Reference
In-Depth Information
Table 10.1 Frames, domains, population, and sample parameters
Frames
Domains
A
B
a
b
ab
Population size
N
A
N
B
N
a
N
b
N
ab
Sample size
n
A
n
B
n
a
n
b
n
ab
t
y
t
y
t
y
Total of y
t
y
t
ab
y
t
HT
,
y
t
HT
,
y
t
HT
,
y
t
HT
,
y
t
a
HT
,
y
,
A
,
t
a
HT
,
y
,
B
HT estimator of the total of y
t
y
¼
noted that we could practically assume that
N
b
¼
0, because the spatial
list is exhaustive by definition. The estimator is then decomposed into two parts:
one consisting of a weighted average of the results obtained by the two surveys for a
common portion of the population, and the other that represents a correction factor
to account for the undercoverage of
B
.
The variance of Eq. (
10.41
) can be expressed by (Kott and Vogel
1995
)
n
b
¼
þ
þ ʱ
¼
2
Var t
HT
,
y
t
HT
,
y
t
HT
,
y
2
Var
t
a
HT
,
y
,
A
Var
Var
þ
ð
1
ʱ
Þ
:
ð
10
:
42
Þ
t
a
HT
,
y
,
B
t
HT
,
y
;t
a
HT
,
y
,
A
t
HT
,
y
;t
a
HT
,
y
,
B
Var
þ
2
ʱ
Cov
þ
21
ð
ʱ
Þ
Cov
Assuming uniform survey costs (which is quite unrealistic but useful for better
understanding the approaches without getting lost in excessive mathematical
details), and assuming that the sample sizes are fixed, the value of
ʱ
that minimizes
Eq. (
10.42
)is
t
a
HT
,
y
,
B
t
HT
,
y
;t
a
HT
,
y
,
A
t
HT
,
y
;t
a
HT
,
y
,
B
Var
Cov
þ
Cov
ʱ
¼
:
ð
10
:
43
Þ
t
a
HT
,
y
,
A
t
a
HT
,
y
,
B
Var
þ
Var
Equation (
10.43
) represents the coefficient that uses a weighted average to opti-
mally integrate the two surveys. Recent research within multiple frames has
considered the theoretical properties of the estimators, and has proposed several
alternatives to Eqs. (
10.41
)-(
10.43
) (Bankier
1986
; Skinner
1991
; Skinner
et al.
1994
; Lohr and Rao
2000
,
2006
; Mecatti
2007
; Singh and Mecatti
2011
).
Recently, many NSIs have been making important investments into building
frames of farms that integrate administrative data and should provide basic infor-
mation for the coordination and integration of all agricultural statistical surveys.
The coverage rate of these surveys and the update of the frames are critical for
ensuring that the frame does not become prematurely obsolete. The only technique
that currently appears to be able to fulfill this task is a spatial sampling that is based
on the land, which can be used for direct observations of crop acreage and yields,
and to estimate and update the coverage of the list frame.
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