## The Annals of Statistics

- Ann. Statist.
- Volume 36, Number 1 (2008), 403-427.

### Endogenous post-stratification in surveys: Classifying with a sample-fitted model

F. Jay Breidt and Jean D. Opsomer

#### Abstract

Post-stratification is frequently used to improve the precision of survey estimators when categorical auxiliary information is available from sources outside the survey. In natural resource surveys, such information is often obtained from remote sensing data, classified into categories and displayed as pixel-based maps. These maps may be constructed based on classification models fitted to the sample data. Post-stratification of the sample data based on categories derived from the sample data (“endogenous post-stratification”) violates the standard post-stratification assumptions that observations are classified without error into post-strata, and post-stratum population counts are known. Properties of the endogenous post-stratification estimator are derived for the case of a sample-fitted generalized linear model, from which the post-strata are constructed by dividing the range of the model predictions into predetermined intervals. Design consistency of the endogenous post-stratification estimator is established under mild conditions. Under a superpopulation model, consistency and asymptotic normality of the endogenous post-stratification estimator are established, showing that it has the same asymptotic variance as the traditional post-stratified estimator with fixed strata. Simulation experiments demonstrate that the practical effect of first fitting a model to the survey data before post-stratifying is small, even for relatively small sample sizes.

#### Article information

**Source**

Ann. Statist., Volume 36, Number 1 (2008), 403-427.

**Dates**

First available in Project Euclid: 1 February 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1201877307

**Digital Object Identifier**

doi:10.1214/009053607000000703

**Mathematical Reviews number (MathSciNet)**

MR2387977

**Zentralblatt MATH identifier**

1132.62006

**Subjects**

Primary: 62D05: Sampling theory, sample surveys

Secondary: 62F12: Asymptotic properties of estimators

**Keywords**

Calibration classification design consistency generalized linear model Horvitz–Thompson estimator ratio estimator stratification survey regression estimator

#### Citation

Breidt, F. Jay; Opsomer, Jean D. Endogenous post-stratification in surveys: Classifying with a sample-fitted model. Ann. Statist. 36 (2008), no. 1, 403--427. doi:10.1214/009053607000000703. https://projecteuclid.org/euclid.aos/1201877307