SCIPRESS J. Japan Statist. Soc.

J. Japan Statist. Soc., Vol. 32 (No. 1), pp. 43-55, 2002

Assessment of Influence of Individual Observations on Prediction Mean Square Errors in Variable Selection Problems

Hidekazu Takeuchi

Abstract. A new influence measure is proposed to assess the influence of individual observations on prediction mean square errors (PMSE) in variable selection problems. It is based on the estimated PMSE which consists of Cook's distance and Mallows' CP statistic. Another interpretation of Cook's distance is also given through the expression of the new influence measure. Illustrative examples show the effectiveness of the new influence measure.

Key words and phrases: Cook's distance, influence measure, influential observation, Mallows' CP statistic, regression diagnostics, sensitivity analysis.

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