Open Access
March, 1983 Properties of Estimators of Quadratic Finite Population Functions: The Batch Approach
T. P. Liu, M. E. Thompson
Ann. Statist. 11(1): 275-285 (March, 1983). DOI: 10.1214/aos/1176346078


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.


Download Citation

T. P. Liu. M. E. Thompson. "Properties of Estimators of Quadratic Finite Population Functions: The Batch Approach." Ann. Statist. 11 (1) 275 - 285, March, 1983.


Published: March, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0508.62013
MathSciNet: MR684885
Digital Object Identifier: 10.1214/aos/1176346078

Primary: 62D05

Keywords: Admissibility , complex sampling estimation , sampling , surveys , unbiased minimum variance estimation

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • March, 1983
Back to Top