Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Least absolute deviation estimator based consistent model selection in regression

  • Shende, K.S. (Department of Statistics, Shivaji University) ;
  • Kashid, D.N. (Department of Statistics, Shivaji University)
  • Received : 2018.11.28
  • Accepted : 2019.03.20
  • Published : 2019.05.31
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Abstract

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.

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References

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