Estimation in Functional Regression for General Exponential Families

Joint with David Pollard, Harrison Zhou

Annals of Statistics (2012) Vol. 40, No.5, 2421-2451

This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinitedimensional 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-ofmeasure argument, inspired by Le Cam’s theory of asymptotic equivalence, is used to eliminate the bias caused by the nonlinearity of exponential family models.