Kelly Toppin
National Agricultural Statistics Service, United States Department of Agriculture
Estimated Covariance Matrices Associated with Calibration
Luca Sartore
National Institute of Statistical Sciences
Kelly Toppin
National Agricultural Statistics Service, United States Department of Agriculture
Clifford Spiegelman
Texas A&M University
Surveys often provide numerous estimates of population parameters. Some of the population values may be known to lie within a small range of values with a high level of certainty. Calibration is used to adjust survey weights associated with the observations within a data set. This process ensures that the ``sample'' estimates for the target population totals (benchmarks) lie within the anticipated ranges of those population values. The additional uncertainty due to the calibration process needs to be captured. In this paper, some methods for estimating the variance of the population totals are proposed for an algorithmic calibration process based on minimizing the $L_1$-norm relative error. The estimated covariance matrices for 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.