# One standard error rule for variable selection

Breiman et al recommend the 1-SE rule, and show that it is successful in screening out noise variables. At page no. 80 of their book, I get confuse about the '1 S.E. Rule'. $$R'[T(k_l)]\leq R'[T(k_0)]+S.E\{R'[T(k_0)]\}$$

Where $T_1, T_2, ...$ are the number of sequence of trees (number of variables) and the corresponding estimates of K-fold cross validation prediction error are $R'[T_1], R'[T_2], ...$ Then, the tree selected is $T(k_l)$, where $k_l$ is the maximum $k$ satisfying above equation. Please note that $R'[T(k_0)]=min_kR'[T_k]$

My question is that how I will calculate the $S.E\{R'[T(k_0)]\}$ ? because it is only one value, Please correct me where I am wrong.

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Isn't it as simple as calculating error of mean of $R'[T_i]$ (for a given i) using each cross validation fold as an "independent" measurement? (i.e. calculating standard deviation of $R'[T_i]$ (across K folds) and then dividing by $\sqrt{K-1}$ gives a reasonable resampling-based proxy of that standard error)
what are $i$ and $K$? – Biostat Nov 22 '11 at 17:56
Can I use the following estimate for SE? $SD(X_m)$, where $X_m=mean(R[T_i])$ and $m$ denote replication of k-fold CV. – Biostat Nov 22 '11 at 18:45