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Dissertation_Sgambellone.pdf (2.53 MB)

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Use of Ranking Information From Unmeasured Units in Ranked Set and Judgement Post Stratified Samples

Sgambellone, Anthony James
http://rave.ohiolink.edu/etdc/view?acc_num=osu1386001520

Abstract Details

2013, Doctor of Philosophy, Ohio State University, Statistics.
Judgement post-stratified (JPS) and ranked set sampling (RSS) are known to produce samples that are often 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 JPS and RSS do not use all potential information that unmeasured observations may contribute. We introduce new estimators that incorporate this information on the stochastic relationship between ranks of measured units and information from unmeasured units. For example, our estimator uses the knowledge that a measurement from a unit in the third judgement class is expected to be larger than measurements from units in the second and first judgement classes. We first propose nonparametric estimators for the population cumulative distribution function (cdf) and order statistic cdfs, based on the conditional expected value of the empirical cdf. Existing methods use only the fully measured values in calculating the empirical cdf. Our proposed estimator uses the measured values and the conditional expectation of the unmeasured values, given the rank and value of the measured unit. The estimator is constructed through an iterative procedure. An initial estimate of the cdf is used to estimate the conditional expectations used in calculation of our estimator and the ranking probabilities are calculated from estimates of the judgement class cdfs using the procedure in Ozturk (2008). This process is repeated until the iterative procedure converges. We show that under mild conditions the estimator is consistent and conditionally unbiased. Simulations indicate that this new estimator is more efficient than selected benchmark estimators for nearly all RSS designs, but greatest benefit is obtained under JPS for samples with empty judgement classes. In addition, estimates of the order statistic cdfs are obtained. Next we introduce moment estimation that uses the conditional expected values of the unmeasured units, given the measured unit from that set. This allows the estimators to be conditionally unbiased even for severely unbalanced samples. The conditional expected moment is calculated for each set, given the one measured value from that set. The mean of the conditional expected set moments is then used to estimate the sample moment. Finally, this moment estimator is used to estimate population parameters according to the relation between distribution parameters and population moments. An initial estimate of the parameters is used in estimation of the conditional expected values, and the process is iterated until convergence. The degree of benefit that our moment estimator provides in comparison to existing methods varies by distribution, but the greatest benefits are seen for samples with empty judgement classes.
Omer Ozturk (Advisor)
Elizabeth Stasny (Advisor)
Steve MacEachern (Committee Member)
170 p.
Statistics
RSS; JPS; Order Statistics; Ranking Information; Ranked Set Sample; Judgement Post Stratification

Recommended Citations

Citations

  • Sgambellone, A. J. (2013). Use of Ranking Information From Unmeasured Units in Ranked Set and Judgement Post Stratified Samples [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1386001520

    APA Style (7th edition)

  • Sgambellone, Anthony. Use of Ranking Information From Unmeasured Units in Ranked Set and Judgement Post Stratified Samples. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1386001520.

    MLA Style (8th edition)

  • Sgambellone, Anthony. "Use of Ranking Information From Unmeasured Units in Ranked Set and Judgement Post Stratified Samples." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1386001520

    Chicago Manual of Style (17th edition)

osu1386001520
521
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.