The Annals of Statistics

Semiparametric Estimation of Normal Mixture Densities

Kathryn Roeder

Full-text: Open access

Abstract

A semiparametric method for estimating densities of normal mean mixtures is presented. This consistent data-driven method of estimation is based on probability spacings. The estimation technique involves iteratively fixing the standard deviation of the normal kernel that serves as a smoothing parameter, and then maximizing a function of the probability spacings over all mixing distributions. Based on the distribution of uniform spacings, a distribution free goodness-of-fit criterion is developed to guide the selection of the smoothing parameter. The result is a set of consistent estimators indexed by a range of smoothing parameters. Empirical process results are used to prove consistency.

Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 929-943.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348664

Digital Object Identifier
doi:10.1214/aos/1176348664

Mathematical Reviews number (MathSciNet)
MR1165600

Zentralblatt MATH identifier
0746.62044

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G30: Order statistics; empirical distribution functions 62E20: Asymptotic distribution theory

Keywords
Confidence set of densities normal mixtures semiparametric density estimation spacings

Citation

Roeder, Kathryn. Semiparametric Estimation of Normal Mixture Densities. Ann. Statist. 20 (1992), no. 2, 929--943. doi:10.1214/aos/1176348664. https://projecteuclid.org/euclid.aos/1176348664


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