Extensions of calibration estimators in survey sampling

Estimators from the family of calibration estimators are often used when auxiliary information about a population is available. By viewing calibration as an algebraic problem, this article extends the: calibration technique to estimate population parameters other than totals and means, and also extends the technique to the case where there is no solution to the calibration equation. These extensions permit the development of estimators for small domains that have a synthetic component and yet good asymptotic properties. A new method to compute a calibration estimator that uses an arbitrary distance measure is developed. This method points to a new path for the investigation of the properties of the estimator. It is shown how through the Kronecker product the calibration method can be used to estimate variances and domain totals, Monte Carlo studies show that important improvements in the precision of variance estimators are possible with use of the calibration method. Necessary and sufficient conditions for the existence of weights that satisfy the calibration equation are also given.