Subset selection in multiple linear regression with heavy tailed error distribution
Many subset selection methods in a multiple linear regression context such as Mallow's C p -statistic are based on the Least squares (LS) estimator of regression coefficients. Whenever the distribution of the error variable is non-normal or heavy tailed, the LS estimator is known to perform 'poorly' and hence a method based on this estimator obviously selects a wrong subset. In this article, we propose a new criterion called N p -criterion for subset selection in a multiple linear regression model whenever the distribution of error variable is heavy tailed. The new criterion is based on the nonparametric estimator of regression coefficients. The method is illustrated with examples simulated from a class of distributions such as laplace, Slash and mixture of normal distributions and it is demonstrated that in all these cases, it selects proper subsets while the classical subset selection methods such as C p -statistic fail to do so. Further, it is shown that the proposed method is also useful whenever the data contains an influential or outlier observation.
subset selection multiple linear regression nonparametric estimator outlier