Type
Text
Type
Dissertation
Advisor
Zhu, Wei | Jiao, Xiangmin | Hu, Jiaqiao | Li, Ellen.
Date
2011-12-01
Keywords
Statistics
Department
Department of Applied Mathematics and Statistics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71254
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
The 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. | 107 pages
Recommended Citation
Han, Hao, "Least Sine Squares and Robust Compound Regression Analysis" (2011). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 460.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/460