Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 139

selected in more than one sample. For example, the unit in position ( k ) of iteration
k may be the same as the unit in position ( l ) of iteration l , k l . Mcintyre ( 1952 )

proposed an estimation of y U (i.e. y U , RSS ) using the average of the y ( k ) k s , which is
unbiased and independent from possible ranked errors. In this case the variance is

6 ¼

X

n
i ¼1 ʼ i:n , y

2

y U

y
n

¼ ˃

V y U , RSS ; ð 6 : 25 Þ

n 2

where ʼ i : n , y is the average of the i -th order statistic of an SRS of size n (Dell and

Clutter 1972 ). From Eq. ( 6.25 ), RSS is clearly more efficient than SRS.
The result is purely non-parametric, and it is assumed that the ranking costs are
negligible. There are several extensions of Eq. ( 6.25 ) for some parametric models
(see, among many others, Sinha et al. 1996 ). Because RSS becomes more difficult
as n increases, Patil et al. ( 1994 ) introduced the notion of cycles to improve the
method when the efficiency of the estimates leads to considerably large samples.

6.10 Adaptive Sampling

The efficiencies of classical sampling plans for agricultural surveys are effectively
limited because the spatial distribution of the study variable is highly irregular,
particularly when conducted on spatial units. Furthermore, sometimes the popula-
tion units are extremely rare and follow a clustered pattern. These populations are
common in many environmental and natural resource studies, and also in agricul-
tural statistics. For example, a survey for estimating floricultural or horticultural
products should be appropriate for the small size of the fields cultivated with these
crops and their concentration in few zones of a country. Thus, the probability of
randomly selecting such fields is very low and, as a consequence, the uncertainty of
the estimates will be so large that they will be considered unacceptable. Note that
this example regards two products whose characteristics are also important from an
economic point of view, because of their extremely high yield.
There are several designs that can be adapted to survey rare populations. The
design choice depends on the survey objectives and the distribution of the popula-
tion to be sampled. However, every design cannot perform well for small sample
sizes in which the units are very rare and are found in very small groups (Christman
2009 ).
If a census or administrative data can be used to determine the spatial pattern of
the variable in advance, a conventional design such as stratified sampling may
reduce the negative effects. This is particularly the case if a specific and efficient
stratification can be produced using a reasonable amount of time and resources.
However, the patterns are not typically known in advance and the use of an adaptive
design may be more appropriate.