# 7. Auxiliary Data and Ratio Estimation

Published Online: 10 FEB 2012

DOI: 10.1002/9781118162934.ch7

Copyright © 2012 John Wiley & Sons, Inc.

Book Title

## Sampling, Third Edition

Additional Information

#### How to Cite

Thompson, S. K. (2012) Auxiliary Data and Ratio Estimation, in Sampling, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118162934.ch7

#### Publication History

- Published Online: 10 FEB 2012
- Published Print: 23 FEB 2012

#### Book Series:

#### Book Series Editors:

- Walter A. Shewhart and
- Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780470402313

Online ISBN: 9781118162934

- Summary
- Chapter

### Keywords:

- auxiliary information;
- finite-population central limit theorem;
- ratio estimator;
- simple random sampling;
- unequal probability designs

### Summary

Auxiliary information may be used either in the sampling design or in estimation. Ratio and regression estimators are examples of the use of auxiliary information in estimation. This chapter first examines the ratio estimator in the traditional, design-based context, in which the y- and x-values for each unit in the population are viewed as fixed and probability is involved only through the sample selection procedure. The ratio estimator is considered first when the design is simple random sampling and then more generally under unequal probability designs. The chapter then presents derivations and approximations for the ratio estimator and discusses finite-population central limit theorem for the ratio estimator. Finally, it discusses the implications of the model-based approach to both estimation and design.

#### Controlled Vocabulary Terms

central limit theorem; estimator; probability; Random sampling; Ratio estimator