Statistical Inference in a Simple Linear Model Under Microaggregation

A problem statistical offices are increasingly faced with is
guaranteeing confidentiality when releasing microdata sets. One
method to provide safe microdata is to reduce the information
content of a data set by means of masking procedures. A widely
discussed masking procedure is microaggregation, a technique where
observations are grouped and replaced with their corresponding
group means. However, while reducing the disclosure risk of a data
file, microaggregation also affects the results of statistical
analyses. We focus on the effect of microaggregation on a simple
linear model. In a previous paper we have shown how to correct for
the aggregation bias of the naive least-squares estimator that
occurs when the dependent variable is used to group the data. The
present paper deals with the asymptotic variance of the corrected
least-squares estimator and with the asymptotic variance of the
naive least-squares estimator when either the dependent variable or
the regressor is used to group the data. We derive asymptotic
confidence intervals for the slope parameter. Furthermore, we show
how to test for the significance of the slope parameter by
analyzing the effect of microaggregation on the asymptotic power
function of the naive t-test.