Journal of Official Statistics, Vol.19, No.2, 2003. pp. 119131

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Optimal Calibration Estimators Under Two-Phase Sampling

Optimal calibration estimators require in general complete auxiliary information. When such information is not available, the estimation procedure can be combined with two-phase sampling where a large, less costly first-phase sample measured over the auxiliary variables is used to get estimates for certain population quantities related to the covariates. In this article we propose optimal calibration estimators for the population mean, the distribution function, the population variance and other second-order finite population quantities under two-phase sampling. The proposed optimal calibration estimators for a second-order finite population quantity such as the population variance can ideally be used to obtain more efficient variance estimators for a first-order finite population quantity such as the total or the distribution function. The estimation strategy can be applied to various measurement error and non-response problems. The design-based finite sample performances of proposed estimators are investigated through a simulation study using real survey data from the 1996 Statistics Canada Family Expenditure (FAMEX) Survey.

Auxiliary information; measurement error; model-assisted approach; nonresponse; variance estimation.

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