Advances in Sampling Estimation - Sampling Spatial Units for Agricultural Surveys - page 242

> q2obs < - as.numeric(cut(yobs,quantile(yobs,probs seq ¼

+ (0,1,0.2))))
> q2obs[is.na(q2obs)] < -1
> framepop $ xc2 < - framepop $ xc^2
> framepop $ yc2 < - framepop $ yc^2
> framepop < - cbind(framepop,yobs,q1obs,q2obs)
> srs < - srswor(n,N)
> framesrs < - framepop[srs ¼¼ 1,]
> dsrs < - svydesign(id ¼ ~1,data ¼ framesrs,fpc ¼ ~rep(n/N,n))
> popfreq < - table(q1obs ¼ framepop $ q1obs)
> psdsrs < - postStratify(dsrs, strata ¼ ~q1obs,population ¼ popfreq)
> estps < - svytotal(~yobs, psdsrs, deff ¼ TRUE)

> estps

total SE DEff
yobs 90280.8 1944.9 0.956

10.3 Calibration Estimator

The definition of coherence constraints in the estimation process is a remarkable
operation that can lead to a sensible reduction of the variance of the estimates.
Its success crucially depends on the correlation between the covariates X subject
to constraints and the variables of interest y. When the statistical unit is a farm or
other legal body, these covariates are essentially concerned with structural aspects
and size. It is reasonable to assume that these data affect information collected from
the farms. We may be confident that the reliability gain arising from the use of these
specific auxiliaries can be considered as guaranteed. This argument is perhaps even
more compelling with respect to surveys of spatial units, because the auxiliaries
represent the same variable observed with different devices: the human eye, a
digital map, or a satellite sensor.
A further advantage of imposing constraints on the estimates is that we can set
some limits on the results that mitigate strong variations and irregularities caused
by anomalous units.
Furthermore, it is appropriate to distinguish the case where the imposed con-
straints are coming from a frame (and therefore can be considered as known,
controlled, and not affected by sampling errors) from that in which the auxiliary
information is derived from the survey estimates. In the first case, the improvement
is ensured. However, uncertainties about constraints due to sampling errors may
affect the results in the second case. Then, we should be extremely careful when
imposing constraints so that we avoid introducing a bias into the estimation process,
which could seriously affect the quality of the results.