The Annals of Statistics

Local likelihood density estimation

Clive R. Loader

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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:

Article information

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

First available in Project Euclid: 17 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Density estimation local likelihood local polynomials


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

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