Bootstrap Aggregation for CrossValidation and Inference under Constraints 
Dr. Peter Hall
Monday, April 9, 2007
4:10 p.m.
223 Weber
ABSTRACT
A major asset of the crossvalidation approach to smoothingparameter choice is its utilitarian character. However, the bandwidths produced by crossvaldiation are relatively noisy, and this difficulty impedes good performance. The stochastic variability of crossvalidation can be reduced significantly by using bootstrap aggregation, or bagging, a method proposed by Breiman (1999). The technique is very simple to use, and enjoys the utilitarian character of crossvalidation. For instance, it can be applied in practically all of the many settings where crossvalidation is employed for bandwidth choice with the aim of optimising an $L_2$ measure of performance.
Arbitrarily large reductions in bandwidth variability are theoretically possible, although in practice bagging would likely be used relatively modestly. In particular, halfsample bagging can reduce bandwidth variability by approximately 50%. We shall also discuss a baggingbased approach to constrained inference, for example to parameter estimation when it is known that the true value of the parameter satisfies an inequality constraint.
