Functional Regression for General Exponential Families

Functional Regression for General Exponential Families By

Nonparametric Regression in Exponential Families by Lawrence

Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In this paper we consider nonparametric regression in exponential families with the main focus on the natural exponential families with a quadratic variance funct...

Nonparametric Regression in Natural Exponential Families

Abstract: Theory and methodology for nonparametric regression have been particularly well developed in the case of additive homoscedastic Gaussian noise. Inspired by asymptotic equivalence theory, there have been ongoing efforts in recent years to construct explicit procedures that turn other function estimation problems into a standard nonparametric regression with Gaussian noise. Then in prin...

Estimation in Functional Regression for General Exponential Families by Winston

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 g...

Exponential Dispersion Models and the Gauss-Newton Algorithm

It is well known that the Fisher scoring iteration for generalized linear models has the same form as the Gauss-Newton algorithm for normal regression. This note shows that exponential dispersion models are the most general families to preserve this form for the scoring iteration. Therefore exponential dispersion models are the most general extension of generalized linear models for which the a...