Article,
p Values for High-Dimensional Regression
Journal of The American Statistical Association, 104 (488): 1671--1681 (2009)
DOI: 10.1198/jasa.2009.tm08647
Abstract
Assigning signicance in high-dimensional regression is challenging. Most computationally ecient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder (2008) which splits the data into two parts. The number of variables is then reduced to a manageable size using the rst split, while classical variable selection techniques can be applied to the remaining variables, using the data from the second split. This yields asymptotic error control under minimal conditions. It involves, however, a one-time random split of the data. Results are sensitive to this arbitrary choice: it amounts to a \textbackslashp-value lottery" and makes it dicult to reproduce results. Here, we show that inference across multiple random splits can be aggregated, while keeping asymptotic control over the inclusion of noise variables. In addition, the proposed aggregation is shown to improve power, while reducing the number of falsely selected variables substantially
Tags
- comparisons,
- control,
- dimensionality,
- error
- high
- multiple
- p-value,
- regularization,
- selection
- variable
- \_tablet\_modified,
