## The Classical Ratio Estimator

### by James R. Knaub, Jr.

**Abstract:**
The classical ratio estimator (CRE) is very simple, has a long history, and has a stunningly broad range of application, especially with regard to survey statistics, particularly establishment survey statistics. The CRE has a number of desirable properties, one of which is that the sum of its estimated residuals is always zero. It is easily extended to multiple regression, and a property shown in Sarndal, Swensson and Wretman (1992) may be used to indicate the desirability of this zero sum of estimated residuals feature when constructing regression weights for multiple regression. In the single regressor form, the zero sum of estimated residuals property is related to an interesting phenomenon expressed in Fox (1997). Finally, relationships of the CRE to some other statistics are also considered.
**Key Words:** estimated residuals; weighted least squares; ordinary least squares; heteroscedasticity

**Author:**

James R. Knaub, Jr., james.knaub@eia.doe.gov

**Editor:**
Avner Bar-Hen, avner@bar-hen.net

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