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Activity Number: 504
Type: Contributed
Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #306838
Title: Robust Compound Regression: A New Approach for Robust Estimation of Errors-in-Variables Models
Author(s): Hao Han*+ and Yeming Ma and Xiangmin Jiao and Ling Leng and Zhengrong Liang and Wei Zhu
Companies: SUNY at Stony Brook and National Institutes of Health and SUNY at Stony Brook and SUNY at Stony Brook and SUNY at Stony Brook and SUNY at Stony Brook
Address: , Stony Brook, NY, , United States
Keywords: Errors-in-variables model ; robust regression ; nonparametric regression ; least sine squares ; robust compound regression ; regression efficiency

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 adopted in applied sciences. The traditional EIV model estimators, however, can be highly biased by outliers and other departures from the underlying assumptions.

In this paper, we develop a novel nonparametric regression approach - the robust compound regression (RCR) analysis method for the robust estimation of EIV models. We first introduce a robust and efficient estimator called least sine squares (LSS). Taking full advantage of both the new LSS method and the compound regression analysis method developed in our own group, we subsequently propose the RCR approach as a generalization of those two, which provides a robust counterpart of the entire class of the maximum likelihood estimation (MLE) solutions of the EIV model, in a 1-1 mapping. Technically, our approach gives users the flexibility to select from a class of RCR estimates the optimal one with a predefined regression efficiency criterion satisfied. Simulation studies and real-life examples are provided to illustrate the effectiveness of the RCR approach.

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