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Phd dissertation Jinguo Gao 2013.pdf (1.37 MB)

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Rank Regression in Order Restricted Randomized Designs

Gao, Jinguo
http://rave.ohiolink.edu/etdc/view?acc_num=osu1374099460

Abstract Details

2013, Doctor of Philosophy, Ohio State University, Statistics.
One of the main principles in designing an experiment is to use blocking factors whenever it is possible. In many studies, blocking information is not precisely defined or may be subjective in nature. Hence, it is usually discarded in the construction of the design and in the analysis of a data set. This research uses a special design, and order restricted randomized design (ORRD), which uses available subjective information in a small set of experimental units, to create a judgment ranked blocking factor. Under this design, we first select a small set of experimental units and rank units within each set pre-experimentally from smallest to largest based on inherent variation. The ranking process induces a positive correlation structure for the within-set residuals. Under the design, we then use a randomization scheme to assign the treatment levels to the ranked experimental units. Such an assignment with certain restrictions on the randomization scheme, which keeps the design to be balanced, translates the within-set positive dependence structure into a variance reduction technique in the estimation of a contrast parameter. Chapter 1 provides a literature review on designs that are closely related to the one we proposed. It then introduces two types of designs for ORRDs. This chapter also provides a discussion on similarities and differences between ORRDs and generalized randomized block designs. Chapter 2 introduces an additive model to analyze ORRD data. The parameter of this model is estimated with a rank regression estimator. It is shown, under some regularity conditions, that the asymptotic distribution of the rank regression estimator converges to a p-dimensional multivariate normal distribution. Chapter 3 develops statistical inference to test generalized linear hypotheses. We consider three tests: drop, score and Wald tests. Under some regularity conditions, we show that the test statistics of these three tests converge to a chi-squared distribution with appropriate degrees of freedom. For moderate sample sizes, the distributions of these statistics under the null hypothesis can be approximated with an F-distribution with appropriate degrees of freedom. Chapters 4 and 5 address some computational issues and provide empirical evidence for the performance of the tests. The empirical evidence indicates that the Type I error rates of the tests are reasonably close to the nominal size 0.05 under a wide range of simulation conditions. The empirical power study also indicates that the tests constructed based on ORRDs outperform the tests constructed based on completely randomized designs. Chapter 6 illustrates the use of the proposed estimators and tests by applying them to a clinical trial data set. Chapter 7 provides concluding remarks and discusses some open problems for future studies.
Omer Ozturk, Dr. (Advisor)
Steve MacEachern, Dr. (Committee Member)
Elizabeth Stasny, Dr. (Committee Member)
154 p.
Statistics
rank regression; order restricted randomized designs; statistical tests; simulation

Recommended Citations

Citations

  • Gao, J. (2013). Rank Regression in Order Restricted Randomized Designs [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1374099460

    APA Style (7th edition)

  • Gao, Jinguo. Rank Regression in Order Restricted Randomized Designs . 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1374099460.

    MLA Style (8th edition)

  • Gao, Jinguo. "Rank Regression in Order Restricted Randomized Designs ." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1374099460

    Chicago Manual of Style (17th edition)

osu1374099460
1,149
© 2013, some rights reserved.Creative Commons License Rank Regression in Order Restricted Randomized Designs by Jinguo Gao is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.