## The Annals of Statistics

### Using specially designed exponential families for density estimation

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 24, Number 6 (1996), 2431-2461.

Dates
First available in Project Euclid: 16 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032181161

Digital Object Identifier
doi:10.1214/aos/1032181161

Mathematical Reviews number (MathSciNet)
MR1425960

Zentralblatt MATH identifier
0878.62028

Subjects
Primary: 62F05: Asymptotic properties of tests 62G05: Estimation

#### Citation

Efron, Bradley; Tibshirani, Robert. Using specially designed exponential families for density estimation. Ann. Statist. 24 (1996), no. 6, 2431--2461. doi:10.1214/aos/1032181161. https://projecteuclid.org/euclid.aos/1032181161

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• STANFORD UNIVERSITY TORONTO, ONTARIO
• STANFORD, CALIFORNIA 94305 CANADA