Search Results

Robust estimation of the prediction variance discusses the issues that arise when model misspecification is second order. That is, when the second order moments of the working model for the population are incorrect, as is typically the case. Here balanced sampling is of no avail, and alternative, more robust, methods of prediction variance must be used. This chapter focuses on development of these methods for the case where the working population model is the ratio model, as well as when a general linear predictor is used and the working model has quite general first and second order moments. The case of a clustered population with unknown within cluster heteroskedasticity is also discussed and the ultimate cluster variance estimator derived.

When there is a single continuous auxiliary variable, it is often reasonable to assume a simple linear regression model relating this variable to the variable of interest. This chapter describes the use of regression population models in sample surveys. Proportional models, where the intercept is assumed to be zero, have a long history in survey sampling and are discussed first. Empirical best and best linear unbiased predictors are derived. The ratio model is a special case of the proportional model, and this leads to the well known ratio estimator. Models with intercepts are then discussed, including best estimators of totals. Sample designs are developed. Under the ratio model, the optimal design is to select only the units with the largest values of the auxiliary variable. However this would not be robust to departures from the ratio model. The problem of robust design is discussed in Chapter 8. Optimal design is also discussed for the linear model with intercept. The combination of regression and stratification is discussed. It is possible to assume the same regression or ratio relationship in every stratum, or to allow different coefficients in each stratum. Data from an agriculture survey are used to illustrate this choice.

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.