The Annals of Statistics

Local likelihood density estimation

Clive R. Loader

Full-text: Open access

Abstract

Local likelihood was introduced by Tibshirani and Hastie as a method of smoothing by local polynomials in non-Gaussian regression models. In this paper an extension of these methods to density estimation is discussed, and comparison with other methods of density estimation presented. The local likelihood method has particularly strong advantages over kernel methods when estimating tails of densities and in multivariate settings. Suppose constraints are incorporated in a simple manner. Asymptotic properties of the estimate are discussed. A method for computing the estimate is outlined.

C code to implement the estimation procedure described in this paper, together with S interfaces for graphical display of results, are available at:

http://cm.bell-labs.com/stat/project/locfit/index.html

Article information

Source
Ann. Statist. Volume 24, Number 4 (1996), 1602-1618.

Dates
First available in Project Euclid: 17 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1032298287

Mathematical Reviews number (MathSciNet)
MR1416652

Digital Object Identifier
doi:10.1214/aos/1032298287

Zentralblatt MATH identifier
0867.62034

Subjects
Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties 62H12: Estimation

Keywords
Density estimation local likelihood local polynomials

Citation

Loader, Clive R. Local likelihood density estimation. Ann. Statist. 24 (1996), no. 4, 1602--1618. doi:10.1214/aos/1032298287. http://projecteuclid.org/euclid.aos/1032298287.


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  • MURRAY HILL, NEW JERSEY 07974-2070 E-MAIL: clive@bell-labs.com