Advances in Sampling Estimation - Sampling Spatial Units for Agricultural Surveys - page 237

derive the variance of the HT estimator of the total for the basic and most widely
used designs (see Chap. 6 ) . In practice, agencies and institutions are often faced
with complex surveys that involve non-linear target parameters (we can avoid
having to use Eqs. ( 1.27 ) and ( 1.30 ) of Sect. 1.2 by estimating a ratio) or highly
complex designs. The design complexity may refer to the number of basic design
characteristics that we must consider (as described in Chap. 6 ) , and the number of
estimation features (e.g., adjustments for nonresponses and undercoverage, large
observation or outlier detection procedures, post-stratification, and ratio or regres-
sion estimators). This last situation is different from a basic survey, which may
involve only one or two of these estimation and design features. Alternative
variance estimation procedures (which may be approximate) are needed to avoid
dependences on the above-mentioned factors.
Finally, it is convenient to consider that practical agricultural surveys are rarely
performed only on list frames (farms, households, or other legal bodies), or only on
spatially defined frames, but also using a combination of these two types of frames.
This dichotomy is overtaken not by the statistical advantages that a frame could
have with respect to the other (see Chap. 5 ), but by the evidence that some
important phenomena are only measurable on a specific statistical unit. Income,
or any other economical aspects of agricultural activities, cannot be observed on a
polygon, and the soil moisture or any other chemical measurements cannot be
assigned to the farmer. As a result, a complete system of surveys should be
necessarily based on several statistical unit definitions, and possibly be integrated
to estimate the common variables. This strategy is known as multiple frames.
This chapter is organized as follows. Section 10.2 outlines the need to enhance
the estimation process by efficiently introducing auxiliary information. These
considerations are then extended and generalized within the calibration approach
in Sect. 10.3 . Then, in Sect. 10.4 , we briefly summarize the main features of the
nonresponse adjustment problem and the solutions proposed in the literature, while
in Sect. 10.5 we review the techniques for variance estimation. In Sect. 10.6 , the
multiple frame approach to survey sampling is described together with some simple
estimator. Finally, the last section contains our conclusions. The R codes for the
main estimators are included in the text, and some examples of estimating the total
and variance from an artificial population are shown.
10.2 Using Auxiliary Information to Improve
the Estimation
When estimating finite-population parameters, the most popular approach is a
design-based inference that implicitly uses the HT estimator. However, even in
this rigorous context, statistical models can be introduced, and generally play an
important role in the inference. The main modeling issue is to improve the precision
of the HT estimator by introducing covariates that contain additional information