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Estimation in Functional Regression for General Exponential Families


  • Winston Wei Dou
  • David Pollard
  • Harrison H. Zhou


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 non-linearity of exponential family models.

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  • Winston Wei Dou & David Pollard & Harrison H. Zhou, 2011. "Estimation in Functional Regression for General Exponential Families," Papers 1108.3552,
  • Handle: RePEc:arx:papers:1108.3552

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    References listed on IDEAS

    1. Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December.
    2. Jose E. Figueroa-Lopez & Martin Forde, 2011. "The small-maturity smile for exponential Levy models," Papers 1105.3180,, revised Dec 2011.
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