Estimation in functional regression for general exponential families
Abstract
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension grows with sample size. A change-of-measure argument, inspired by Le Cam's theory of asymptotic equivalence, is used to eliminate the bias caused by the nonlinearity of exponential family models.
Cite
@article{arxiv.1001.3742,
title = {Estimation in functional regression for general exponential families},
author = {Winston Wei Dou and David Pollard and Harrison H. Zhou},
journal= {arXiv preprint arXiv:1001.3742},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOS1027 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)