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Estimation Optimality of Corrected AIC and Modified Cp in Linear Regression
Author(s) -
Davies Simon L.,
Neath Andrew A.,
Cavanaugh Joseph E.
Publication year - 2006
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2006.tb00167.x
Subject(s) - akaike information criterion , mathematics , estimator , unbiased estimation , statistics , linear regression , u statistic , minimum variance unbiased estimator
Summary Model selection criteria often arise by constructing unbiased or approximately unbiased estimators of measures known as expected overall discrepancies (Linhart & Zucchini, 1986, p. 19). Such measures quantify the disparity between the true model (i.e., the model which generated the observed data) and a fitted candidate model. For linear regression with normally distributed error terms, the “corrected” Akaike information criterion and the “modified” conceptual predictive statistic have been proposed as exactly unbiased estimators of their respective target discrepancies. We expand on previous work to additionally show that these criteria achieve minimum variance within the class of unbiased estimators.