Nonparametric maximum likelihood estimation of a mixing distribution
Abstract
The nonparametric maximum likelihood estimate of a mixing distribution is shown to be self-consistent, a property which characterizes the nonparametric maximum likelihood estimate of a distribution function in incomplete data problems. Under various conditions the estimate is a step function, with a finite number of steps. Its computation is illustrated with a small example.
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NPML procedures provide a discrete distribution based on a finite number of mass points.
“NPML procedures provide a discrete distribution that is based on a finite number of mass points (Laird, 1978; Böhning, 2005).”
From A Re-Evaluation of Random-Effects Meta-Analysis (2009) · cites this paper as Laird, 1978
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References 33 · Cited by 753
- Authors
- Laird, N.
- Affiliations
- Harvard University (US)
- Corresponding author
- Laird, Nan
- ORCID
- Laird, Nan
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1978-12
- Volume
- 73
- Issue
- 364
- Pages
- 805-811
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1997817781
- Cited by
- 753
- References
- 33
- Citations by year
- 2026: 12 · 2025: 19 · 2024: 14 · 2023: 8 · 2022: 21 · 2021: 23 · 2020: 19 · 2019: 17 · 2018: 18 · 2017: 23 · 2016: 31 · 2015: 14 · 2014: 28 · 2013: 24 · 2012: 36
- FWCI
- 1.54
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- nonparametric maximum likelihood estimation, mixing distribution, self-consistency, missing data, mixture models, distribution function estimation
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