A0336
Title: A resized parametric bootstrap method for inference of a high-dimensional generalized linear model
Authors: Qian Zhao - University of Massachusetts, Amherst (United States) [presenting]
Emmanuel Candes - Stanford (United States)
Abstract: Accurate statistical inference can be challenging when the ratio between the number of parameters and the sample size is not negligible. One example is logistic regression: when the number of parameters increases with the sample size, approximations based on either classical asymptotic theory or bootstrap are grossly off the mark. A resized bootstrap method is introduced to infer model parameters from a logistic regression in arbitrary dimensions. As in the parametric bootstrap, observations from a distribution are resampled, which depends on an estimated regression coefficient sequence. The novelty is that this estimate is actually far from the maximum likelihood estimate (MLE). The estimate is obtained by appropriately shrinking the MLE towards the origin. The amount of shrinkage is motivated by recent theories of high-dimensional MLEs. It is demonstrated that the resized bootstrap method yields valid confidence intervals in both simulated and real data examples. It is further shown that the resized bootstrap method extends to other high-dimensional generalized linear models.
