Conditional predictive inference post model selection

Details Conditional predictive inference post model selection Conditional predictive inference post model selection

2009-08-25

arxiv.org/abs/0908.3615v1

Annals of Statistics 2009, Vol. 37, No. 5B, 2838-2876

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS660 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/08-AOS660

We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important explanatory variables can be infinite, where no regularity conditions are imposed on unknown parameters, where the number of explanatory variables in a "good" model can be of the same order as sample size and where the number of candidate models can be of larger order than sample size. The performance of inference procedures is evaluated conditional on the training sample. Under weak conditions on only the number of candidate models and on their complexity, and uniformly over all data-generating processes under consideration, we show that a certain prediction interval is approximately valid and short with high probability in finite samples, in the sense that its actual coverage probability is close to the nominal one and in the sense that its length is close to the length of an infeasible interval that is constructed by actually knowing the "best" candidate model. Similar results are shown to hold for predictive inference procedures other than prediction intervals like, for example, tests of whether a future response will lie above or below a given threshold.

Affiliated with

Also associated with

No associations

Rating

Conditional predictive inference post model selection does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Conditional predictive inference post model selection, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conditional predictive inference post model selection will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-233330