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RATIO ESTIMATION AND FINITE POPULATIONS: SOME RESULTS DEDUCIBLE FROM THE ASSUMPTION OF AN UNDERLYING STOCHASTIC PROCESSAustralian & New Zealand Journal of Statistics, 5
- Publisher
- Springer Journals
- Copyright
- Copyright © 2001 by Science Press
- Subject
- Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/BF02669697
- Publisher site
- See Article on Publisher Site
Abstract
This paper sheds light on an open problem put forward by Cochran[1]. The comparison between two commonly used variance estimators $$v_1 (\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{R} )$$ and $$v_2 (\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{R} )$$ of the ratio estimator $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{R} $$ for population ratioR from small sample selected by simple random sampling is made following the idea of the estimated loss approach (See [2]). Considering the superpopulation model under which the ratio estimator $$\hat \bar Y_R $$ for population mean $$\overline Y $$ is the best linear unbiased one, the necessary and sufficient conditions for $$\upsilon _1 (\hat R)\mathop \succ \limits^u \upsilon _2 (\hat R)$$ and $$\upsilon _2 (\hat R)\mathop \succ \limits^u \upsilon _1 (\hat R)$$ are obtained with ignored the sampling fractionf. For a substantialf, several rigorous sufficient conditions for $$\upsilon _2 (\hat R)\mathop \succ \limits^u \upsilon _1 (\hat R)$$ are derived.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 5, 2007