of bias interact in complex ways, so that it is difficult to characterize the appropriate level of aggregation for poststratification. Numerical examples show that cell control, row control, column control, or no control may be best depending on the parameter settings and population quantity of interest. Control on both margins through some kind of raking procedure was not treated here but is worthy of further consideration.
The results in this paper indicate that the Census Bureau’s plan for control at a fine level of demographic stratification within estimation areas may be problematic. It may yield estimators with bias properties worse than no controls at all.
This paper is only a first step in evaluation of the possible effects of errors in postcensal population controls on ACS estimates. Research is needed in a number of directions. First, the numerical results are limited and the parameter values in that limited study were chosen to illustrate potential problems, which may or may not occur in real ACS data. For example, the artificial population has cell means that vary by a factor of 10, which may or may not be realistic in ACS applications. It is necessary to explore a range of parameter values (response probabilities, coverage probabilities, cell means, postcensal population estimation bias, etc.) that are plausible in real ACS applications to determine whether or not the potential problems identified in this paper are real problems for the ACS.
Second, the numerical experiments focus exclusively on bias, because bias is a major reason for poststratification and because the independence assumptions under which variances are derived in this paper are possibly unrealistic. Certainly bias is critical, and in many applications it dominates variance. Ultimately, the interest is mean squared error, the sum of squared bias and variance. To study variance analytically, it is necessary to make some assumptions about the covariance structure for the various types of errors (for example, assumptions about correlations among postcensal population estimation errors in different cells, or between postcensal population estimation errors and frame imperfections). These assumptions should be guided by a careful consideration of the ACS and the methods of postcensal population estimation. Analytic computations under these assumptions could be supplemented or replaced by simulations.
Finally, this paper does not explore the full complexity of the weighting factors used for the ACS, so the issue of bias would need further study, both analytical and empirical, in this more complex setting.
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