Abstract
Subset selection is a long-standing problem. One goal of a selection procedure is consistency. Consistency using Akaike's Final Prediction Error Criterion (FPE) as a selection procedure can be shown to be related to the cost complexity parameter in FPE. However, another goal of a selection procedure is accurate predictions. The consistency property does not necessarily guarantee this second objective. The issue can be thought of as a bias versus variance tradeoff for the procedure. We use the bootstrap to model this tradeoff and provide an objective way of choosing a procedure which attempts to balance the two objectives. This is done in the spirit of the cost complexity pruning algorithm of classification and regression trees. The methodology is described and illustrated on simulated and real data examples.
| Original language | English |
|---|---|
| Pages (from-to) | 273-287 |
| Number of pages | 15 |
| Journal | Statistica Sinica |
| Volume | 9 |
| Issue number | 1 |
| State | Published - Jan 1 1999 |
| Externally published | Yes |
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Keywords
- Adaptive estimation
- Mallow's C
- Model selection
- Prediction error
- Resampling methods
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
Cite this
Bootstrap choice of cost complexity for better subset selection. / Rao, Jonnagadda S.
In: Statistica Sinica, Vol. 9, No. 1, 01.01.1999, p. 273-287.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Bootstrap choice of cost complexity for better subset selection
AU - Rao, Jonnagadda S
PY - 1999/1/1
Y1 - 1999/1/1
N2 - Subset selection is a long-standing problem. One goal of a selection procedure is consistency. Consistency using Akaike's Final Prediction Error Criterion (FPE) as a selection procedure can be shown to be related to the cost complexity parameter in FPE. However, another goal of a selection procedure is accurate predictions. The consistency property does not necessarily guarantee this second objective. The issue can be thought of as a bias versus variance tradeoff for the procedure. We use the bootstrap to model this tradeoff and provide an objective way of choosing a procedure which attempts to balance the two objectives. This is done in the spirit of the cost complexity pruning algorithm of classification and regression trees. The methodology is described and illustrated on simulated and real data examples.
AB - Subset selection is a long-standing problem. One goal of a selection procedure is consistency. Consistency using Akaike's Final Prediction Error Criterion (FPE) as a selection procedure can be shown to be related to the cost complexity parameter in FPE. However, another goal of a selection procedure is accurate predictions. The consistency property does not necessarily guarantee this second objective. The issue can be thought of as a bias versus variance tradeoff for the procedure. We use the bootstrap to model this tradeoff and provide an objective way of choosing a procedure which attempts to balance the two objectives. This is done in the spirit of the cost complexity pruning algorithm of classification and regression trees. The methodology is described and illustrated on simulated and real data examples.
KW - Adaptive estimation
KW - Mallow's C
KW - Model selection
KW - Prediction error
KW - Resampling methods
UR - http://www.scopus.com/inward/record.url?scp=0033441210&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0033441210&partnerID=8YFLogxK
M3 - Article
VL - 9
SP - 273
EP - 287
JO - Statistica Sinica
JF - Statistica Sinica
SN - 1017-0405
IS - 1
ER -