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The Support Reduction Algorithm for Computing Non‐Parametric Function Estimates in Mixture Models

Author

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  • PIET GROENEBOOM
  • GEURT JONGBLOED
  • JON A. WELLNER

Abstract

. In this paper, we study an algorithm (which we call the support reduction algorithm) that can be used to compute non‐parametric M‐estimators in mixture models. The algorithm is compared with natural competitors in the context of convex regression and the ‘Aspect problem’ in quantum physics.

Suggested Citation

  • Piet Groeneboom & Geurt Jongbloed & Jon A. Wellner, 2008. "The Support Reduction Algorithm for Computing Non‐Parametric Function Estimates in Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 385-399, September.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:3:p:385-399
    DOI: 10.1111/j.1467-9469.2007.00588.x
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    References listed on IDEAS

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    1. SIMAR, Leopold, 1976. "Maximum likelihood estimation of a compound Poisson process," LIDAM Reprints CORE 271, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Mette Langaas & Bo Henry Lindqvist & Egil Ferkingstad, 2005. "Estimating the proportion of true null hypotheses, with application to DNA microarray data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 555-572, September.
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    Cited by:

    1. Yining Chen & Richard J. Samworth, 2016. "Generalized additive and index models with shape constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 729-754, September.
    2. Rufibach, Kaspar, 2010. "An active set algorithm to estimate parameters in generalized linear models with ordered predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1442-1456, June.
    3. Azadbakhsh, Mahdis & Jankowski, Hanna & Gao, Xin, 2014. "Computing confidence intervals for log-concave densities," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 248-264.
    4. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    5. Dümbgen, Lutz & Mösching, Alexandre & Strähl, Christof, 2021. "Active set algorithms for estimating shape-constrained density ratios," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    6. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    7. Feng, Oliver Y. & Chen, Yining & Han, Qiyang & Carroll, Raymond J & Samworth, Richard J., 2022. "Nonparametric, tuning-free estimation of S-shaped functions," LSE Research Online Documents on Economics 111889, London School of Economics and Political Science, LSE Library.
    8. repec:jss:jstsof:36:i02 is not listed on IDEAS
    9. Chee, Chew-Seng, 2017. "A mixture model-based nonparametric approach to estimating a count distribution," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 34-44.
    10. Jiaying Gu & Roger Koenker & Stanislav Volgushev, 2017. "Testing for homogeneity in mixture models," CeMMAP working papers CWP39/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Fadoua Balabdaoui & Jon A. Wellner, 2010. "Estimation of a k‐monotone density: characterizations, consistency and minimax lower bounds," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 45-70, February.
    12. Durot, Cécile & Huet, Sylvie & Koladjo, François & Robin, Stéphane, 2013. "Least-squares estimation of a convex discrete distribution," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 282-298.

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