The Annals of Statistics
- Ann. Statist.
- Volume 20, Number 2 (1992), 929-943.
Semiparametric Estimation of Normal Mixture Densities
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
http://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. http://projecteuclid.org/euclid.aos/1176348664.
