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Three Essays in Quantitative Analysis

Dong, Zhiyuan
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1282048935

Abstract Details

2010, PhD, University of Cincinnati, Business: Business Administration.
Essay 1: We develop a matrix approach via an eigen analysis for comparing the variances of estimates of a population total based on the arc-weight, Horvitz-Thompson, and conventional methods under a many-to-many frame structure on a data free basis. A benefit of this representation is that it results in an improved method for computing the 1st order inclusion probabilities for the Horvitz-Thompson method, which is known to be computationally expensive to obtain in a many-to-many context. We also propose an improved method for characterizing the eigen-structure of the Arc-Weight method. A Mathematica based package that performs the corresponding analysis is developed to facilitate the computations. Essay 2: We propose a constrained M-estimation approach in logistic regression models to improve prediction accuracy in situations where useful prior information is available in the form of linear inequality and equality constraints on the parameters. While our approach is intended for use in small to moderate sample size situations, it also has practical virtues in helping to avoid the issue of non-convergence of parameter estimates. We also supply large sample size properties of the estimators, i.e., consistency and asymptotic distributions under certain assumptions. We apply the constrained approach on a real corporate bankruptcy prediction data set by embedding prior information such as Moody and S and P credit ratings and demonstrate that the prediction results are promising. We also conduct a simulation study and obtain favorable prediction performance via several metrics over the traditional approach. Essay 3: In this essay, we develop a sample average approach to estimate the optimal coverage probability in an optimal coverage problem. We demonstrate the statistical properties in estimation bias reduction of this approach and provide some asymptotic results. We report the results of an empirical study on our proposed approach.
Martin Levy, PhD (Committee Chair)
Yan Yu, PhD (Committee Member)
Jeffrey Camm, PhD (Committee Member)
James Cochran, PhD (Committee Member)
Tim Keyes, PhD (Committee Member)
117 p.
Statistics
population element; estimators; ¿¿¿¿¿¿¿

Recommended Citations

Citations

  • Dong, Z. (2010). Three Essays in Quantitative Analysis [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1282048935

    APA Style (7th edition)

  • Dong, Zhiyuan. Three Essays in Quantitative Analysis. 2010. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1282048935.

    MLA Style (8th edition)

  • Dong, Zhiyuan. "Three Essays in Quantitative Analysis." Doctoral dissertation, University of Cincinnati, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1282048935

    Chicago Manual of Style (17th edition)

ucin1282048935
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© 2010, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.