Estimation in Functional Regression for General Exponential Families
The Annals of Statistics. Volume 40, Number 5 (2012), pp. 2421-2451
31 Pages Posted: 20 Jun 2013 Last revised: 25 Jan 2020
Date Written: March 30, 2012
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.
Keywords: Approximation of compact operators, Assouad’s lemma, exponential families, functional estimation, minimax rates of convergence
JEL Classification: C1, C2, C4, C5
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