Preprint #97-30
On Adaptive Function Estimation
by
Yuhong Yang
Abstract
General results on adaptive function estimation are obtained with respect
to a collection of estimation strategies for both density estimation and
nonparametric regression under square L_2 loss. It is shown that without
knowing which strategy in a given countable collection works best for the
underlying function, a single strategy can be constructed by mixing the
proposed ones so that it is adaptive in terms of an average cumulative
risk. An implication is that under some mild conditions, a minimax-rate
adaptive estimator exists for a given countable collection of function
classes, i.e., a single estimator can be constructed to be simultaneously
minimax optimal in terms of rates of convergence for all the function classes
being considered. Examples for high-dimensional function estimation are
provided.
Copies of preprints are available from the author upon request.
Use the preprint number (located at the top of the page) and make the
request directly to the author, Iowa State University, Department of
Statistics, Snedecor Hall, Ames, IA 50011-1210.