TY - JOUR
T1 - Prediction/estimation with simple linear models
T2 - Is it really that simple?
AU - Yang, Yuhong
PY - 2007/2
Y1 - 2007/2
N2 - Consider the simple normal linear regression model for estimation/ prediction at a new design point. When the slope parameter is not obviously nonzero, hypothesis testing and information criteria can be used for identifying the right model. We compare the performances of such methods both theoretically and empirically from different perspectives for more insight. The testing approach at the conventional size of 0.05, in spite of being the "standard approach," performs poorly in estimation. We also found that the frequently told story "the Bayesian information criterion (BIC) is good when the true model is finite-dimensional, and the Akaike information criterion (AIC) is good when the true model is infinite-dimensional" is far from being accurate. In addition, despite some successes in the effort to go beyond the debate between AIC and BIC by adaptive model selection, it turns out that it is not possible to share the pointwise adaptation property of BIC and the minimax-rate adaptation property of AIC by any model selection method. When model selection methods have difficulty in selection, model combining is a better alternative in terms of estimation accuracy.
AB - Consider the simple normal linear regression model for estimation/ prediction at a new design point. When the slope parameter is not obviously nonzero, hypothesis testing and information criteria can be used for identifying the right model. We compare the performances of such methods both theoretically and empirically from different perspectives for more insight. The testing approach at the conventional size of 0.05, in spite of being the "standard approach," performs poorly in estimation. We also found that the frequently told story "the Bayesian information criterion (BIC) is good when the true model is finite-dimensional, and the Akaike information criterion (AIC) is good when the true model is infinite-dimensional" is far from being accurate. In addition, despite some successes in the effort to go beyond the debate between AIC and BIC by adaptive model selection, it turns out that it is not possible to share the pointwise adaptation property of BIC and the minimax-rate adaptation property of AIC by any model selection method. When model selection methods have difficulty in selection, model combining is a better alternative in terms of estimation accuracy.
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U2 - 10.1017/S0266466607070016
DO - 10.1017/S0266466607070016
M3 - Article
AN - SCOPUS:33947417700
SN - 0266-4666
VL - 23
SP - 1
EP - 36
JO - Econometric Theory
JF - Econometric Theory
IS - 1
ER -