Survey Methodology
Model based inference using ranked set samples

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by Omer Ozturk and Konul Bayramoglu KavlakNote 1

  • Release date: June 21, 2018
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Abstract

This paper develops statistical inference based on super population model in a finite population setting using ranked set samples (RSS). The samples are constructed without replacement. It is shown that the sample mean of RSS is model unbiased and has smaller mean square prediction error (MSPE) than the MSPE of a simple random sample mean. Using an unbiased estimator of MSPE, the paper also constructs a prediction confidence interval for the population mean. A small scale simulation study shows that estimator is as good as a simple random sample (SRS) estimator for poor ranking information. On the other hand it has higher efficiency than SRS estimator when the quality of ranking information is good, and the cost ratio of obtaining a single unit in RSS and SRS is not very high. Simulation study also indicates that coverage probabilities of prediction intervals are very close to the nominal coverage probabilities. Proposed inferential procedure is applied to a real data set.

Key Words:      Ranked set sampling; Finite population; Mean square prediction error; Sampling cost model; Coherent ranking; Concomitant ranking; Visual ranking.

Table of contents

How to cite

Ozturk, O., and Bayramoglu, K. (2018). Model based inference using ranked set samples. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 44, No. 1. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2018001/article/54925-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Copyright

Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2018

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

Ottawa

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Sampling designs
Section 3. Unbiased estimators
Section 4. Cost model
Section 5. Empirical results
Section 6. Example
Section 7. Concluding remarks
Acknowledgements
Appendix
References

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