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Least absolute deviation estimator based consistent model selection in regression
Communications for Statistical Applications and Methods 2019;26:273-293
Published online May 31, 2019
© 2019 Korean Statistical Society.

K. S. Shende1,a, D. N. Kashida

aDepartment of Statistics, Shivaji University, India
Correspondence to: 1Department of Statistics, Shivaji University, Kolhapur, India (MS).
E-mail: shendeks.stat99@gmail.com
Received November 28, 2018; Revised February 20, 2019; Accepted March 20, 2019.
We consider the problem of model selection in multiple linear regression with outliers and non-normal error distributions. In this article, the robust model selection criterion is proposed based on the robust estimation method with the least absolute deviation (LAD). The proposed criterion is shown to be consistent. We suggest proposed criterion based algorithms that are suitable for a large number of predictors in the model. These algorithms select only relevant predictor variables with probability one for large sample sizes. An exhaustive simulation study shows that the criterion performs well. However, the proposed criterion is applied to a real data set to examine its applicability. The simulation results show the proficiency of algorithms in the presence of outliers, non-normal distribution, and multicollinearity.
Keywords : linear regression, model selection, consistency, robustness, sequential algorithm