@article{d623fad36486460c83b24c20d6510113,
title = "A Smooth nonparametric estimate of a mixing distribution using mixtures of gaussians",
abstract = "We propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of Gaussians subject to the constraint that the component variances be greater than or equal to some minimum value h. This approach can lead to estimates of many shapes, with smoothness controlled by parameter h. We show that the resulting estimate will always be a finite mixture of Gaussians, each having variance h. The nonparametric maximum likelihood estimate can be viewed as a special case, with h = 0. The method can be extended to estimate multivariate mixing distributions. Examples and the results of a simulation study are presented.",
keywords = "Deconvolution, Empirical bayes, Longitudinal data, Mixed models, Mixtures, Random effects",
author = "Magder, {Laurence S.} and Zeger, {Scott L.}",
note = "Funding Information: Laurence Magder is Assistant Professor, Department of Epidemiology and Preventive Medicine, University of Maryland, Baltimore, MD 21201. Scott Zeger is Professor, Department of Biostatistics, The Johns Hopkins University, Baltimore, MD 21205. This work was supported by a Program Grant from MERCK Research Laboratories. The authors thank Bruce Lindsay for suggesting a key idea in the proof of Theorem I, and the National Institutes of Health for Grant ISI0RR06460 (N. DeClaris, PI) for computer support. The data for the example were collected by the Multicenter AIDS Cohort Study with Centers (Principal Investigators) at The Johns Hopkins School of Public Health (Alfred Saah, Alvaro Munoz); Northwestern University Medical School (John Phair); University of California, Los Angeles (Roger Detels); and University of Pittsburgh (Charles Rinaldo). The study is funded by the National Institute of Allergy and Infectious Disease and the National Cancer Institute.",
year = "1996",
month = sep,
day = "1",
doi = "10.1080/01621459.1996.10476984",
language = "English (US)",
volume = "91",
pages = "1141--1151",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "435",
}