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The Interpretation of Mallows's $C_p$-Statistic

Steven G. Gilmour
Journal of the Royal Statistical Society. Series D (The Statistician)
Vol. 45, No. 1 (1996), pp. 49-56
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2348411
Stable URL: http://www.jstor.org/stable/2348411
Page Count: 8
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The Interpretation of Mallows's $C_p$-Statistic
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Abstract

When selecting variables in multiple-regression studies, the model with the lowest value of Mallows's $C_p$-statistic is often chosen. It is shown here that when the estimate of $\sigma^2$ comes from the full model an adjusted $C_p, \bar{C}_p$, has the property that $E(\bar{C}_p) = p$. It is suggested that a procedure be adopted which involves testing whether the model with minimum $\bar{C}_p$ is really better than a simpler model. Tables approximating the null distribution of the test statistics are given.

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