Agriculture Reference
In-Depth Information
Conclusions
Calibration, and in general the introduction of auxiliary variables in the
estimation process, is a purely randomization-based technique. Auxiliary
information on benchmark variables can be used to reduce the variability of
many survey variables (y). This is because of the random selection of the
sample and not the goodness of fit of an assumed superpopulation model.
However, this approach can be extended to more general nonlinear models or
used to calibrate totals that are not known but estimated by other surveys. It
can clearly move very quickly from a design-based inference to a model-
based inference, in which the model is the basic component of a prediction
approach to survey sampling (see Chap. 12 ).
The risk of this approach is that a practitioner may wish to add as many
constraints as possible to a calibration estimator, so that they have used all the
available information. However, this does not consider the covariates that are
more related to the survey variables, or those with a propensity to non-
responses. A better choice is to use an algorithm that chooses the best
constraints.
Traditional Taylor linearization can severely underestimate the true vari-
ability, even if its asymptotic behavior for large sample sizes without non-
responses should be similar to resampling methods. In particular, the
jackknife estimator is identical to the Taylor linearization variance estimator
up to the second-order, and the bootstrap provides more reliable standard
estimates than the jackknife and the BRR. These results suggest that the
choice of estimator should depend more on operational, rather than statistical,
considerations. In practice, the bootstrap may be preferred, because it is more
flexible, it avoids the analytical work of Taylor linearization, and it does not
have the limiting constraints of BRR and jackknife.
For a detailed account on the asymptotic properties, and a review of the
asymptotic comparisons of different resampling methods, see Shao and
Tu ( 1995 ).
Multiple frame designs can give better coverage and precision than a
single frame survey with an equivalent cost, because all units in the
overlapping frames have a positive inclusion probability. The survey must
be carefully designed to realize these cost savings.
Misclassification in one of the overlapping domains can create serious
biases, regardless of the estimator. In general, the optimal design is a function
of sampling variances and non-sampling errors in each frame, and of the
chosen estimator. In a multiple frame survey, domain misclassification
effects, nonresponses, and mode biases are often confounded.
Multiple frame survey estimation clearly depends on combining estimates
from overlapping domains. This method assumes that the estimators in ab
from the two surveys are both estimating the same quantity. If, however, A is
(continued)
 
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