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Thesis of Wencan He.pdf (901.59 KB)

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Statistical Inference for Binormal ROC Curves under a Density Ratio Model

He, Wencan
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1481298529631999

Abstract Details

2016, Doctor of Philosophy, University of Toledo, Mathematics.
The binormal ROC curve is a classic model for ROC curves. Originally, its functional form is derived from test results that are normally distributed in the diseased and non-diseased populations. However, since the ROC curve pertains to the relationships between two populations rather than to the distributions themselves, the binormal ROC curve applies in more general settings. In this study, we focus on semi-parametric inferences of binormal ROC curves under a density ratio model. Density ratio models have a natural connection with generalized linear model, which has been widely used in biostatistics and other areas of applied statistics. First, by deriving a two-sample density ratio model of the diseased and non-diseased populations from the binormal ROC model, we propose a semi-parametric estimator of binormal ROC curve (called pseudo empirical likelihood non-iterative method or pelni method). Our pelni method is proven that the limiting distribution of pelni is normal. It is shown via a simulation study that pelni method surpasses the fully parametric and nonparametric methods in terms of robustness and efficiency. Since the pelni method only uses the empirical distribution function of the non-diseased sample to estimate the unknown transformation, it is less efficient than other semi parametric methods such as the mle and pmle method by Cai & Moskowitz [2004], especially when sample sizes are small. An analysis of two real examples is presented. To improve the stability of pelni method, we propose a pseudo empirical likelihood (pel) estimator. It is proven that the limiting distribution of our pel estimator is also normal. Via a simulation study, we show that pel is more robust than a fully parametric approach and is more accurate than a fully nonparametric approach. Simulation also shows that, our pel method is more efficient than the pmle method by Cai & Moskowitz [2004], and is quite comparable to their mle method. An analysis of two real examples are presented. Hazard function of the survival times is among the most popular methodology in risk measurement. Kernel estimator is a nonparametric method widely applied in biostatistics and economics. Finally, using the strong approximation technique, we propose a kernel estimator for the hazard function. We show that the limiting distribution for the proposed kernel estimator of hazard function is normal. A real data application of kernel smoothing on hazard rate is presented.
Biao Zhang (Committee Chair)
Donald White (Committee Member)
Rong Liu (Committee Member)
Tian Chen (Committee Member)
124 p.
Statistics

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Citations

  • He, W. (2016). Statistical Inference for Binormal ROC Curves under a Density Ratio Model [Doctoral dissertation, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1481298529631999

    APA Style (7th edition)

  • He, Wencan. Statistical Inference for Binormal ROC Curves under a Density Ratio Model. 2016. University of Toledo, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1481298529631999.

    MLA Style (8th edition)

  • He, Wencan. "Statistical Inference for Binormal ROC Curves under a Density Ratio Model." Doctoral dissertation, University of Toledo, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1481298529631999

    Chicago Manual of Style (17th edition)

toledo1481298529631999
797
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This open access ETD is published by University of Toledo and OhioLINK.
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