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

See all articles by Winston Dou

Winston Dou

The Wharton School, University of Pennsylvania

David Pollard

Independent

Harrison Zhou

Statistics Department of Yale University

Date Written: March 30, 2012

Abstract

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

Suggested Citation

Dou, Winston and Pollard, David and Zhou, Harrison, Estimation in Functional Regression for General Exponential Families (March 30, 2012). The Annals of Statistics. Volume 40, Number 5 (2012), pp. 2421-2451. Available at SSRN: https://ssrn.com/abstract=2281981

Winston Dou (Contact Author)

The Wharton School, University of Pennsylvania ( email )

2318 Steinberg Hall - Dietrich Hall
3620 Locust Walk
Philadelphia, PA 19104
United States

David Pollard

Independent ( email )

No Address Available

Harrison Zhou

Statistics Department of Yale University ( email )

P.O. Box 208290
New Haven, CT 06520
United States

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