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dc.contributor.advisorZhu, Weien_US
dc.contributor.authorHan, Haoen_US
dc.contributor.otherDepartment of Applied Mathematics and Statisticsen_US
dc.date.accessioned2013-05-22T17:34:43Z
dc.date.available2013-05-22T17:34:43Z
dc.date.issued1-Dec-11en_US
dc.date.submitted11-Decen_US
dc.identifierHan_grad.sunysb_0771E_10819en_US
dc.identifier.urihttp://hdl.handle.net/1951/59683
dc.description107 pg.en_US
dc.description.abstractThe errors-in-variables (EIV) regression model, being more realistic by accounting for measurement errors in both the dependent and the independent variables, is widely used in econometrics, chemistry, medical, and environmental sciences, etc. The traditional EIV model estimators, however, can be highly biased by outliers and other departures from the underlying assumptions. In this work, we propose two novel nonparametric estimation approaches - the least sine squares (LSS) and the robust compound regression (RCR) analysis methods for the robust estimation of EIV models. The RCR method, as a natural extension and combination of the new LSS method and the compound regression analysis method developed in our own group (Leng and Zhu 2009), provides the robust counterpart of the entire class of the traditional maximum likelihood estimation (MLE) solutions of the EIV model, in a 1-1 mapping. The advantages of both new approaches lie in their intuitive geometric interpretations, their distribution free property, their independence to the ratio of the error variances, and most importantly their robustness to outlier contamination and other violations of distribution assumptions. Monte Carlo studies are conducted to compare these new robust EIV model estimation methods to other nonparametric regression analysis methods including the least squares (LS) regression analysis method, the orthogonal regression (OR) analysis method, the geometric mean regression (GMR) analysis method, and the robust least median of squares (LMS) regression analysis method. Guidelines on which regression methods are suitable under what circumstances are provided through these simulation studies as well. Real-life examples are provided to further illustrate and motivate these new approaches.en_US
dc.description.sponsorshipStony Brook University Libraries. SBU Graduate School in Department of Applied Mathematics and Statistics. Charles Taber (Dean of Graduate School).en_US
dc.formatElectronic Resourceen_US
dc.language.isoen_USen_US
dc.publisherThe Graduate School, Stony Brook University: Stony Brook, NY.en_US
dc.subject.lcshStatisticsen_US
dc.titleLeast Sine Squares and Robust Compound Regression Analysisen_US
dc.typeDissertationen_US
dc.description.advisorAdvisor(s): Zhu, Wei . Committee Member(s): Jiao, Xiangmin ; Hu, Jiaqiao ; Li, Ellen.en_US
dc.mimetypeApplication/PDFen_US


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