Ranked set sampling (RSS) is a sampling scheme which can successfully replace simple random sampling (SRS) in experimental settings where measuring the units of interest is difficult, expensive, or time consuming, but ranking small subsets of units is relatively easy and inexpensive. Under perfect ranking, the statistical inference based on a RSS data is more efficient than the inference based on a SRS data of equal size. In practice, the ranking process is most likely subject to errors, and the efficiency of the inference decreases with the decrease in the quality of the ranking procedure. Thus, the central issue of a parametric inference is to balance the two ideals: efficiency when the ranking is perfect, and robustness when the ranking is imperfect. Typically there is a trade-off between these two ideals. In order to address this issue, we develop robust statistical inference based on a RSS data from a family of discrete distributions. Our inference relies on minimum disparity functions that measure the distance between the empirical and model distributions. We develop a class of estimators obtained by minimizing disparities between the assumed and empirical models. We show that all minimum disparity estimators are asymptotically efficient at the correct model under perfect ranking. We also show that there exists an estimator within this class, the minimum Hellinger distance estimator, that produces substantially smaller bias than the bias of the maximum likelihood estimator under imperfect ranking.
In addition to robust estimation, we also developed a class of testing procedures, referred to as disparity deviance tests, to test certain hypotheses about the parameters of a family of discrete distributions. We show that under perfect ranking, the disparity deviance tests have the same asymptotic null distribution as the likelihood ratio test. Furthermore, we show that the disparity deviance test based on the Hellinger distance is more stable to imperfect ranking than the likelihood ratio test. We provide finite sample simulation results to evaluate the performance of the proposed procedures.
|School:||The Ohio State University|
|School Location:||United States -- Ohio|
|Source:||DAI-B 79/09(E), Dissertation Abstracts International|
|Keywords:||Bias, Hellinger distance, Imperfect ranking, Mean square error, Minimum distance estimation, Robustness|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be