Risk and resampling under model uncertainty
Abstract
In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of the model selection process. We discuss some problems associated with this approach. An alternative scheme is to use a modelaveraged estimator, that is, a weighted average of estimators obtained under different models, as an estimator of a parameter. We show that the risk associated with a Bayesian modelaveraged estimator is bounded as a function of the sample size, when parameter values are fixed. We establish conditions which ensure that a modelaveraged estimator's distribution can be consistently approximated using the bootstrap. A new, dataadaptive, model averaging scheme is proposed that balances efficiency of estimation without compromising applicability of the bootstrap. This paper illustrates that certain desirable risk and resampling properties of modelaveraged estimators are obtainable when parameters are fixed but unknown; this complements several studies on minimaxity and other properties of postmodelselected and modelaveraged estimators, where parameters are allowed to vary.
 Publication:

arXiv eprints
 Pub Date:
 May 2008
 arXiv:
 arXiv:0805.3244
 Bibcode:
 2008arXiv0805.3244C
 Keywords:

 Mathematics  Statistics;
 Statistics  Methodology;
 60F12 (Primary) 60J05;
 62C10;
 62F40 (Secondary)
 EPrint:
 Published in at http://dx.doi.org/10.1214/074921708000000129 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)