Relaxed calibration of survey weights
N. T. Longford
Abstract
Population surveys are nowadays rarely analysed in isolation
from any auxiliary information, often in the form of population
counts, totals and other summaries. Calibration, or benchmarking,
by which the weighted sample totals of auxiliary variables
are matched to their (known) population totals, is widely applied.
Methods for adjusting the weights to satisfy these constraints
involve iterative procedures with unknown finite-sample properties.
We develop an alternative method in which the weights are calibrated
by minimising a quadratic function, requiring no iterations
and yielding a unique solution.
The relative priority of each constraint is represented
by a tuning parameter.
The properties of the weights and of the calibration estimator,
as functions of these parameters, are explored analytically
and by simulations.
A connection of the proposed method with ridge calibration is established.
To appear in Survey Methodology 50, 2004.
December 2024.