A MORE GENERAL CRITERION FOR SUBSET SELECTION IN MULTIPLE LINEAR REGRESSION

ABSTRACT

In this article, we propose a more general criterion called S_p -criterion, for subset selection in the multiple linear regression Model. Many subset selection methods are based on the Least Squares (LS) estimator of β, but whenever the data contain an influential observation or the distribution of the error variable deviates from normality, the LS estimator performs ‘poorly’ and hence a method based on this estimator (for example, Mallows’ C_p -criterion) tends to select a ‘wrong’ subset. The proposed method overcomes this drawback and its main feature is that it can be used with any type of estimator (either the LS estimator or any robust estimator) of β without any need for modification of the proposed criterion. Moreover, this technique is operationally simple to implement as compared to other existing criteria. The method is illustrated with examples.

Keywords:

• Multiple linear regression
• Subset selection
• C_p -statistic
• RC _p -statistic
• Huber M-estimator

ACKNOWLEDGMENT

The first author is grateful to University Grants Commission, New Delhi and Western regional office, Pune for awarding Teacher fellowship under the Faculty Improvement Program. We also thank the referee for his constructive comments which led to improvement in the presentation of this paper.