Robust Estimation in Linear Regression with Molticollinearity and Sparse Models

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Abstract:

‎One of the factors affecting the statistical analysis of the data is the presence of outliers‎. ‎The methods which are not affected by the outliers are called robust methods‎. ‎Robust regression methods are robust estimation methods of regression model parameters in the presence of outliers‎. ‎Besides outliers‎, ‎the linear dependency of regressor variables‎, ‎which is called multicollinearity‎, ‎the large number of regressor variables with respect to sample size‎, ‎specially in high dimensional sparse models‎, ‎are problems which result in efficiency reduction of inferences in classical regression methods‎. ‎In this paper‎, ‎we first study the disadvantages of classical least squares regression method‎, ‎when facing with outliers‎, ‎multicollinearity and sparse models‎. ‎Then‎, ‎we introduce and study robust and penalized regression methods‎, ‎as a solution to overcome these problems‎. ‎Furthermore‎, ‎considering outliers and multicollinearity or sparse models‎, ‎simultaneously‎, ‎we study penalized-robust regression methods‎. ‎We examine the performance of different estimators introdused in this paper‎, ‎through three different simulation studies‎. ‎A real data set is also analyzed using the proposed methods‎.

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Journal title

volume 22  issue 2

pages  93- 110

publication date 2018-03

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