Page 80 - Contributed Paper Session (CPS) - Volume 2

CPS1437 Thanyani M.
Fuller (2002) provides an excellent review of the regression related
methods for survey estimation. Regression estimation was first used at
Statistics Canada in 1988 for the Canadian Labour Force Survey. Regression
estimation is now used to construct composite estimators for the Canadian
Labour Force Survey (Gambino, Kennedy and Singh; 2001).
In order to meet the above condition of weight equalisation, constraints
need to be formulated using auxiliary information. This formulation of the
constraints as a set of linear equations with non-negativity requirements
provides important insights into the nature of the problem. In particular, while
in some cases, this set of constraints may have a unique solution, in many
cases there will either be infinite number of possible solutions or there will be
no solution at all.
One of the goals of weighting survey data is to reduce variances in the
estimation procedure by using auxiliary information that is known with a high
degree of accuracy (Mohadjer et al., 1996). Incorporating auxiliary totals to
survey estimates, characteristics in the survey that are correlated with the
auxiliary totals can be estimated with accuracy. Calibration weighting offers a
way to incorporate auxiliary information into survey estimates so that, in
general, characteristics that are correlated with the auxiliary variables are
estimated with greater precision (Reid and Hall, 2001).
The information required for calibration is a set of population control totals
∑ , where is the finite population universe and the are vectors of

auxiliary information that are known individually only for elements in the
respondent sample.
Calibration uses this information by constructing weights such that
∑ = ∑ , where represents the respondent sample and is the

calibrated weight for element . Typically, there are many possible choices of
weights that satisfy this benchmarking constraint. Calibration, by its classical
definition, produces the one that is closest to the design weights, with
closeness determined by a suitable distance function (see Deville et al. (1993),
for details). So selecting a calibration estimator reduces to the selection of a
distance function.
The problem of estimating survey weights can indeed be formulated as a
constrained optimisation problem, when one is attempting to minimise the
difference between the weighted sample distributions of known population
distributions across a set of control variables at both the household and
person-levels. Such constraints can be embedded into a linear programming
problem, with an artificially chosen linear objective function, and solved (at
least in principle) by general linear programming method, such as the Simplex
Algorithm. Within StatMx linear programming is used to achieve the above
objective.

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