The interpretation of Mallows's C_p-statistic

TY - JOUR

T1 - The interpretation of Mallows's Cp-statistic

AU - Gilmour, Steven G.

PY - 1996

Y1 - 1996

N2 - When selecting variables in multiple-regression studies, the model with the lowest value of Mallows's Cp-statistic is often chosen. It is shown here that when the estimate of σ2 comes from the full model an adjusted Cp, C̄p, has the property that E(C̄p) = p. It is suggested that a procedure be adopted which involves testing whether the model with minimum C̄p is really better than a simpler model. Tables approximating the null distribution of the test statistics are given.

AB - When selecting variables in multiple-regression studies, the model with the lowest value of Mallows's Cp-statistic is often chosen. It is shown here that when the estimate of σ2 comes from the full model an adjusted Cp, C̄p, has the property that E(C̄p) = p. It is suggested that a procedure be adopted which involves testing whether the model with minimum C̄p is really better than a simpler model. Tables approximating the null distribution of the test statistics are given.

KW - Multiple regression

KW - Multivariate F-distribution

KW - Variable selection

UR - http://www.scopus.com/inward/record.url?scp=0002527817&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0002527817

SN - 0039-0526

VL - 45

SP - 49

EP - 56

JO - Statistician

JF - Statistician

IS - 1

ER -