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Adaptive Robust Regression Approaches in data analysis and their Applications

Zhang, Zongjun
http://orcid.org/0000-0002-9733-1281
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1445343114

Abstract Details

2015, PhD, University of Cincinnati, Arts and Sciences: Mathematics (Statistics).
In this dissertation, we proposed several novel Adaptive Robust Approaches. The main purpose of the proposed adaptive robust approaches is: (a) To facilitate the decision on whether it is more pertinent to use a robust or a standard technique. (b) To provide an easy but relatively safe alternative to robust approaches without too much struggle about how to choose one among a variety of robust approaches and how to select the parameters (such as trimming portion, tuning constant). The proposed adaptive robust regression approaches are constructed by combining regular robust regressions (such as M-estimators/ LTS ) with application of optimization procedure and characteristics of data in terms of tail weight index(TWI) and normality test. Three main adaptive robust regression approaches are proposed and the related algorithms are also implemented in programs (SAS MACROS and S-PLUS application): (1) Adaptive Robust M-Estimator with optimal tuning constant based on the empirical distribution function (EDF) of the standardized absolute residuals. The algorithm is similar to standard IRWLS, but the TWI and normality test of residuals are investigated to adjust the tuning constant in each iteration within iterative re-weighted least square algorithm (IRWLS) loop. The adaptive approach is implemented in SAS macro %BIWREG()(with Parameter ADAPT=TW). (2) Adaptive Robust M-Estimator with optimal tuning constant based on minimizing the asymptotic variance estimate. Two different algorithms are proposed and compared. The adaptive approaches are implemented in SAS macro %BIWREG(). One is statically adaptive approach (with Parameter ADAPT=AV_S) in which the optimal tuning constant is obtained through many IRWLS processes. The other is dynamically adaptive approach (with Parameter ADAPT=AV_D). (3) Least adaptively trimmed sum of squares estimators with adjusted cut-off (denoted as LATS_AC ). The proposed approach is implemented in the Menu-driven application (Adaptive LTS Regression V.1 in S-Plus). The proposed adaptive robust approaches were demonstrated in both extensive simulation studies and application examples.
Seongho Song, Ph.D. (Committee Chair)
Paul Horn, Ph.D. (Committee Member)
Emily Kang, Ph.D. (Committee Member)
Siva Sivaganesan, Ph.D. (Committee Member)
330 p.
Statistics
Adaptive; Robust; M-Estimator; tuning constant; tail weight index; iterative re-weighted least square algorithm

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Citations

  • Zhang, Z. (2015). Adaptive Robust Regression Approaches in data analysis and their Applications [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1445343114

    APA Style (7th edition)

  • Zhang, Zongjun. Adaptive Robust Regression Approaches in data analysis and their Applications. 2015. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1445343114.

    MLA Style (8th edition)

  • Zhang, Zongjun. "Adaptive Robust Regression Approaches in data analysis and their Applications." Doctoral dissertation, University of Cincinnati, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1445343114

    Chicago Manual of Style (17th edition)

ucin1445343114
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This open access ETD is published by University of Cincinnati and OhioLINK.