Annals of Statistics

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

T. P. Liu and M. E. Thompson

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62D05: Sampling theory, sample surveys

Keywords
Admissibility complex sampling estimation sampling surveys unbiased minimum variance estimation

Citation

Liu, T. P.; Thompson, M. E. Properties of Estimators of Quadratic Finite Population Functions: The Batch Approach. Ann. Statist. 11 (1983), no. 1, 275--285. doi:10.1214/aos/1176346078. https://projecteuclid.org/euclid.aos/1176346078


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