It is easy to get p-values from a linear regression and related methods (t-test, anova, logistic regression), but how can one get p-values in a high dimensional setting (p >> n)? I understand that these problems wouldn't even be solvable, because the necessary collineairity in the data and for the low power. However, it is possible to make very useful models even with high dimensional data, but how to establish any statistical significance?
- how to establish if the two groups are statistically significantly different, based on a high dimensional feature set?
- how to establish if an outcome variable, is statistically significantly related to many input variables?
- How to establish which features are statistically significantly related to an outcome variable, in a model containing many features?
For example, I have a million genes and 200 patients with and without cancer, I want to know if there is an genetic component of this cancer, and if so, which genes are associated.