Downweighting influential clusters in surveys: Application to the 1990 Post Enumeration Survey

Certain clusters may be extremely influential on survey estimates and conse quently contribute disproportionately to their variance, We propose a gener al approach to estimation that downweights highly influential clusters, wit h the amount of downweighting based on M-estimation applied to the empirica l influence of the clusters, The method is motivated by a problem in census coverage estimation, and we illustrate it by using data from the 1990 Post Enumeration Survey (PES). in this context, an objective, prespecified meth odology for handling influential observations is essential to avoid having to justify judgmental post hoc adjustment of weights. In 1990, both extreme weights and large errors in the census led to extreme influence. We estima ted influence by Taylor linearization of the survey estimator, and we appli ed M-estimators based on the t distribution and the Huber psi -function, As predicted by theory, the robust procedures greatly reduced the estimated v ariance of estimated coverage rates, more so than did truncation of weights , On the other hand, the procedure may introduce bias into survey estimates when the distributions of the influence statistics are asymmetric. We cons ider the properties of the estimators in the presence of asymmetry, and we demonstrate techniques for assessing the bias-variance trade-off, finding t hat estimated mean squared error is reduced by applying the robust procedur e to our dataset, We also suggest PES design improvements to reduce the imp act of influential clusters.