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Abstract:
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Surveys often provide numerous estimates of population parameters. Some of the population values may be known, with a high level of certainty, to lie within a small range of values. Calibration is used to adjust the weights associated with observations within a data-set. This process ensures that the "sample" estimates of known population totals (targets) lie within the known ranges of those population values. However, additional uncertainty due to the calibration process needs to be captured. In this paper, some methods to estimate the variance of the population totals are proposed for algorithmic calibration processes based on minimizing the L1-norm relative error. The estimates of the covariance matrix associated with the additional variation of the calibration totals are produced either by linear approximations or bootstrap techniques. Specific data structures are required to allow for the computation of massively large covariance matrices. In particular, the implementation of the proposed algorithms exploits sparse matrices to reduce the computational burden and memory usage. The computational efficiency is shown by a simulation study.
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