NDLI: Nonparametric mean estimation using partially ordered sets

Content Provider	Springer Nature Link
Author	Frey, Jesse
Copyright Year	2012
Abstract	In ranked-set sampling (RSS), the ranker must give a complete ranking of the units in each set. In this paper, we consider a modification of RSS that allows the ranker to declare ties. Our sampling method is simply to break the ties at random so that we obtain a standard ranked-set sample, but also to record the tie structure for use in estimation. We propose several different nonparametric mean estimators that incorporate the tie information, and we show that the best of these estimators is substantially more efficient than estimators that ignore the ties. As part of our comparison of estimators, we develop new results about models for ties in rankings. We also show that there are settings where, to achieve more efficient estimation, ties should be declared not just when the ranker is actually unsure about how units rank, but also when the ranker is sure about the ranking, but believes that the units are close.
Starting Page	309
Ending Page	326
Page Count	18
File Format	PDF
ISSN	13528505
Journal	Environmental and Ecological Statistics
Volume Number	19
Issue Number	3
e-ISSN	15733009
Language	English
Publisher	Springer US
Publisher Date	2012-03-15
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Imperfect rankings Isotonic estimation Judgment post-stratification Ranked-set sampling Ties in rankings Statistics Evolutionary Biology Mathematical and Computational Biology Ecology
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Environmental Science Statistics, Probability and Uncertainty

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