Predictor selection

Michael K. Tippett

International Research Institute for Climate and Society

The Earth Institute, Columbia University

Statistical Methods in Seasonal Prediction, ICTP Aug 2-13, 2010

Ideas

Predictor selection is a nontrivial problem. If you start with too many predictors, you will get in trouble. Overfitting Selection bias, screening.

F-test Mallow’s C_{p}

C_{p} = \frac{SSE_{p}}{S^{2}} − N + 2P

where

SSE_{p} = ∑_{i=1}^{N}(Y_{i} − Y_{pi})^{2}

is the error (sum of squares) for the model with P predictors, Y_{pi} is the predicted value of the i-th observation of Y from the P regressor]]s, *”S”<sup>2</sup> is the residual mean square after [[regression]] on the complete set of ”K” [[regressor]]s * and ”N” is

AIC BIC Split data Cross validation