Combining estimates that are both in error subject to marginal constraints

Abstract

Outside estimates with measures of reliability can be combined with existing tabular estimates of resource statistics to produce new, more precise estimates. But cell estimates do not sum to the original marginal or overall totals when this is done. A method is given to adjust the unchanged cell values to maintain additivity. Classical and bootstrap variance estimators are given for the n × 2 case of combining a cell proportion with an outside estimate assumed to be binomially distributed under fixed marginal constraints, and for the n × m case of combining a cell proportion with a binomially distributed outside estimate under no marginal constraints except that the table total is fixed. For a 3 × 2 test case, a bootstrap variance estimator yielded reliable estimates of precision for the adjusted cell proportions in most cases. For the n × m case, a classical variance estimator was more stable than the bootstrap variance estimators and was less biased than the other variance estimators studied.