Seminars 2007 — Abstracts

Friday, May 18

Speaker: Alan Welsh, ANU

Title: Transformation and smoothing in sample survey data

Abstract: We consider the problem of model-based prediction of a finite population total in the situation that a monotone transformation of the survey variable makes it appropriate to assume additive, homoscedastic errors. As the appropriate transformation to achieve this does not necessarily simultaneously produce an easily parametrised mean function, we assume only that the mean is a smooth function of the auxiliary variable and estimate it nonparametrically. The back transformation of predictions obtained on the transformed scale introduces bias which we remove using smearing (Duan, 1983). We obtain an asymptotic expansion for the prediction error which shows that prediction bias is asymptotically negligible. The expansion shows the effect of smearing on the prediction mean squared error and can be used to compute the asymptotic prediction mean squared error. We propose a model-based bootstrap estimate of the prediction mean squared error. We examine the properties of the predictor and the estimated prediction mean squared error in a small simulation study based on artificial data and on a population constructed from an Australian farm survey.