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Activity Number: 280
Type: Topic Contributed
Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #305562
Title: The Discarded Information of Ranked-Set Sampling and Judgment Post-Stratification
Author(s): Anthony Sgambellone*+ and Omer Ozturk and Elizabeth Stasny
Companies: University of Akron and The Ohio State University and The Ohio State University
Address: 281 Bellewood Ave, Akron, OH, 44311, United States
Keywords: Nonparametric ; Ranked Set Sample ; Judgement Post Stratification ; unbalanced ; estimation
Abstract:

Ranked Set and Judgment Post Stratified Sampling are known to produce samples that are more efficient per measurement than simple random sampling due to the use of auxiliary ranking information of unmeasured units. We believe common estimation methods for RSS and JPS do not use all potential information that unmeasured observations may contribute. We introduce new estimators that incorporate this potential information. Our first proposed estimator, for the population mean, utilizes the expected mean of a set given the measured value within that set. We show this estimator has efficiency close to that of existing methods in the balanced case, with considerable improvement in the unbalanced case. Our second estimator estimates the underlying distribution of each rank and then of the whole population. We show that under mild conditions, the estimate is consistent and asymptotically unbiased. This method performs similarly to the empirical cdf in the balanced case and significantly outperforms it in the unbalanced case.


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