Estimation in Functional Regression for General Exponential Families
AbstractThis 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 non-linearity of exponential family models.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1108.3552.
Date of creation: Aug 2011
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Web page: http://arxiv.org/
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