A MORE GENERAL CRITERION FOR SUBSET SELECTION IN MULTIPLE LINEAR REGRESSION

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...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2002-05, Vol.31 (5), p.795-811
Main Authors: Kashid, D. N., Kulkarni, S. R.
Format: Article
Language:English
Subjects:
Distribution theory
Exact sciences and technology
Huber M-estimator
Linear inference, regression
Mathematics
Multiple linear regression
Parametric inference
Probability and statistics
Sciences and techniques of general use
statistic
Statistics
Subset selection
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Summary: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.
ISSN:0361-0926
1532-415X
DOI:10.1081/STA-120003653