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Activity Number: 651
Type: Contributed
Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #308397
Title: Selection of Shrinkage Estimators for Prediction Out-of-Sample
Author(s): Nina Senitschnig*+ and Hannes Leeb
Companies: and Department of Statistics and OR, University of Vienna
Keywords: prediction ; shrinkage estimators

In a linear regression model with random design, we consider a family of James--Stein-type shrinkage estimators from which we want to select a `good' estimator for prediction out-of-sample. We focus on the challenging situation where the number of explanatory variables can be of the same order as sample size and where the number of candidate estimators can be much larger than sample size. We show that an estimator's out-of-sample performance can differ dramatically from its in-sample performance (which is studied extensively in the existing literature). Using an estimate of the out-of-sample predictive performance, we replace the actual performance by an empirical counterpart and select the empirically best estimator. For Gaussian data, we show that the empirically best estimator is asymptotically as good as the truly best (oracle) estimator, uniformly over a large class of data-generating processes. Moreover, we show that we can estimate the performances of both estimators in a uniformly consistent fashion. These findings extend results of Leeb (2008, Bernoulli 14(3):661--690) where the underlying estimators are least-squares estimators.

Authors who are presenting talks have a * after their name.

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