Open Access
October 2012 Estimation in functional regression for general exponential families
Winston Wei Dou, David Pollard, Harrison H. Zhou
Ann. Statist. 40(5): 2421-2451 (October 2012). DOI: 10.1214/12-AOS1027


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.


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Winston Wei Dou. David Pollard. Harrison H. Zhou. "Estimation in functional regression for general exponential families." Ann. Statist. 40 (5) 2421 - 2451, October 2012.


Published: October 2012
First available in Project Euclid: 4 February 2013

zbMATH: 1373.62155
MathSciNet: MR3097608
Digital Object Identifier: 10.1214/12-AOS1027

Primary: 60K35 , 62J05
Secondary: 62G20

Keywords: Approximation of compact operators , Assouad’s lemma , exponential families , Functional estimation , minimax rates of convergence

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 5 • October 2012
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