Journal
ANNALS OF STATISTICS
Volume 36, Issue 4, Pages 1595-1618Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/009053607000000578
Keywords
model selection; prediction error; lasso
Categories
Ask authors/readers for more resources
We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a preconditioned response variable. The primary method used for this initial regression is supervised principal components. Then we apply a standard procedure such as forward stepwise selection or the LASSO to the preconditioned response variable. In a number of simulated and real data examples, this two-step procedure outperforms forward stepwise selection or the usual LASSO (applied directly to the raw outcome). We also show that under a certain Gaussian latent variable model, application of the LASSO to the preconditioned response variable is consistent as the number of predictors and observations increases. Moreover, when the observational noise is rather large, the suggested procedure can give a more accurate estimate than LASSO. We illustrate our method on some real problems, including survival analysis with microarray data.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available