A New Robust Method for Estimating Linear Regression Model in the Presence of Outliers
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Date
2018
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Publisher
Akamai University, U.S.A
Abstract
Ordinary Least-Squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among response values. Even single atypical value may have a large effect on the parameter estimates. In this paper, we propose a new class of robust regression method for the classical linear regression model. The proposed method was developed using regularization methods that allow one to handle a variety of inferential problems where there are more covariates than cases. Specifically, each outlying point in the data is estimated using case-specific parameter. Penalized estimators are often suggested when the number of parameters in the model is more than the number of observed data points. In light of this, we propose the use of Ridge regression method for estimating the case-specific parameters. The proposed robust regression method was validated using Monte-Carlo datasets of varying proportion of outliers. Also, performance comparison was done for the proposed method with some existing robust methods. Assessment criteria results using breakdown point and efficiency revealed the supremacy of the proposed method over the existing methods considered.
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Keywords
Robust regression, Case indicator, Ridge regression, Outliers
Citation
Pacific Journal of Science and Technology