## Annals of Statistics

### Properties of Estimators of Quadratic Finite Population Functions: The Batch Approach

#### Abstract

Polynomial finite population functions can be expressed as totals over derived populations of batches, or ordered sequences of units from the original population. This paper extends the results of Godambe and Godambe and Joshi on nonexistence of best unbiased estimators and admissibility of the Horvitz-Thompson estimator to the real batch total case. The admissibility results are only partly extendible; an example is given to show that Horvitz-Thompson type estimators of the form $\sum \sum b_{ij}(y_i - y_j)^2/\pi_{ij}$ need not be admissible.

#### Article information

Source
Ann. Statist., Volume 11, Number 1 (1983), 275-285.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346078

Digital Object Identifier
doi:10.1214/aos/1176346078

Mathematical Reviews number (MathSciNet)
MR684885

Zentralblatt MATH identifier
0508.62013

JSTOR