Search Results

Robust prediction under model misspecification focuses on the important topic of how to ensure unbiased prediction even when the assumed population model is not precisely specified. The general role of sample balance in ensuring this unbiasedness is explored in the context of the homogeneous and the ratio population models, and the problem of maintaining a suitable trade-off between prediction efficiency under a working model and unbiasedness under alternative population models is discussed. A general result that provides the necessary conditions for both unbiasedness and efficiency is provided and the extension of balanced sampling to the clustered population model is discussed. A misspecification-robust alternative to balanced sampling is flexible estimation, and the chapter concludes with a development of finite population prediction based on a non-parametric regression fit to the sample data.

Estimation for multipurpose surveys considers the situation of a survey with many output variables and multiple auxiliary variables. In this context, linear estimation based on a single set of multipurpose sample weights represents the dominant approach in sample survey estimation. The development in this chapter includes linear calibrated weighting and ridge weighting, i.e. sample weighting based on a minimum mean squared error ridge regression fit to the survey data, with the latter approach specifically aimed at reducing the incidence of non-positive survey weights caused by sample imbalance and/or model overspecification. The extension to non-parametric regression modelling is also considered, and the important trade-off between sample balance and sample weight variability is discussed.

Model-based inference for distributions and quantiles extends the theory set out in previous chapters to where the target of inference is the finite population distribution function, rather than the finite population total. Inference for quantiles is then carried out by appropriately inverting an efficient predictor of this function. Empirical best predictors under the homogeneous, stratified and linear regression models are described, and their properties discussed. An extension of the empirical best approach to the case where a non-parametric regression fit is more appropriate is developed, as well as an approximation to its prediction variance. An application to imputation for missing data in a wages survey is used to illustrate the comparative performances of the different estimators and the extension to a clustered population model is explored.