Open Access
December 1996 Using specially designed exponential families for density estimation
Bradley Efron, Robert Tibshirani
Ann. Statist. 24(6): 2431-2461 (December 1996). DOI: 10.1214/aos/1032181161


We wish to estimate the probability density $g(y)$ that produced an observed random sample of vectors $y_1, y_2, \dots, y_n$. Estimates of $g(y)$ are traditionally constructed in two quite different ways: by maximum likelihood fitting within some parametric family such as the normal or by nonparametric methods such as kernel density estimation. These two methods can be combined by putting an exponential family "through" a kernel estimator. These are the specially designed exponential families mentioned in the title. Poisson regression methods play a major role in calculations concerning such families.


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Bradley Efron. Robert Tibshirani. "Using specially designed exponential families for density estimation." Ann. Statist. 24 (6) 2431 - 2461, December 1996.


Published: December 1996
First available in Project Euclid: 16 September 2002

zbMATH: 0878.62028
MathSciNet: MR1425960
Digital Object Identifier: 10.1214/aos/1032181161

Primary: 62F05 , 62G05

Keywords: Degrees of freedom , expected deviance , local and global smoothing , moment-matching , Poisson regression

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 6 • December 1996
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