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An Introduction to Model-Based Survey Sampling with Applications$
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Ray Chambers and Robert Clark

Print publication date: 2012

Print ISBN-13: 9780198566625

Published to Oxford Scholarship Online: May 2012

DOI: 10.1093/acprof:oso/9780198566625.001.0001

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Populations with Regression Structure

Populations with Regression Structure

(p.49) 5 Populations with Regression Structure
An Introduction to Model-Based Survey Sampling with Applications

Raymond L. Chambers

Robert G. Clark

Oxford University Press

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.

Keywords:   regression population model, ratio population model, regression estimator, ratio estimator, separate ratio estimator, combined ratio estimator, optimal sample design, robust sample design, heteroskedasticity

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