IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v35y2008i3p385-399.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2007.00588.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2007.00588.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Dümbgen, Lutz & Mösching, Alexandre & Strähl, Christof, 2021. "Active set algorithms for estimating shape-constrained density ratios," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    8. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    9. repec:jss:jstsof:36:i02 is not listed on IDEAS
    10. 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.
    11. 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.
    12. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alfò, Marco & Carbonari, Lorenzo & Trovato, Giovanni, 2023. "On the effects of taxation on growth: an empirical assessment," Macroeconomic Dynamics, Cambridge University Press, vol. 27(5), pages 1289-1318, July.
    2. Van Hanh Nguyen & Catherine Matias, 2014. "On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1167-1194, December.
    3. Shigeyuki Matsui & Hisashi Noma, 2011. "Estimating Effect Sizes of Differentially Expressed Genes for Power and Sample-Size Assessments in Microarray Experiments," Biometrics, The International Biometric Society, vol. 67(4), pages 1225-1235, December.
    4. Payandeh Najafabadi Amir T. & MohammadPour Saeed, 2018. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-31, July.
    5. Axel Gandy & Georg Hahn, 2016. "A Framework for Monte Carlo based Multiple Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1046-1063, December.
    6. Andersson, Thomas & Brännäs, Kurt, 1991. "Explaining Cross-Country Variation in Nationalization Frequencies," Working Paper Series 319, Research Institute of Industrial Economics.
    7. Celisse, Alain & Robin, Stephane, 2008. "Nonparametric density estimation by exact leave-p-out cross-validation," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2350-2368, January.
    8. repec:jss:jstsof:40:i14 is not listed on IDEAS
    9. Han, Bing & Dalal, Siddhartha R., 2012. "A Bernstein-type estimator for decreasing density with application to p-value adjustments," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 427-437.
    10. Seungchul Baek & Junyong Park, 2022. "A computationally efficient approach to estimating species richness and rarefaction curve," Computational Statistics, Springer, vol. 37(4), pages 1919-1941, September.
    11. Ferreira José A. & Berkhof Johannes & Souverein Olga & Zwinderman Koos, 2009. "A Multiple Testing Approach to High-Dimensional Association Studies with an Application to the Detection of Associations between Risk Factors of Heart Disease and Genetic Polymorphisms," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-58, January.
    12. Long Qu & Dan Nettleton & Jack C. M. Dekkers, 2012. "Improved Estimation of the Noncentrality Parameter Distribution from a Large Number of t-Statistics, with Applications to False Discovery Rate Estimation in Microarray Data Analysis," Biometrics, The International Biometric Society, vol. 68(4), pages 1178-1187, December.
    13. Michel Denuit & Claude Lefèvre & Moshe Shaked, 2000. "Stochastic Convexity of the Poisson Mixture Model," Methodology and Computing in Applied Probability, Springer, vol. 2(3), pages 231-254, September.
    14. Chen, Xiongzhi, 2019. "Uniformly consistently estimating the proportion of false null hypotheses via Lebesgue–Stieltjes integral equations," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 724-744.
    15. Montazeri Zahra & Yanofsky Corey M. & Bickel David R., 2010. "Shrinkage Estimation of Effect Sizes as an Alternative to Hypothesis Testing Followed by Estimation in High-Dimensional Biology: Applications to Differential Gene Expression," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-33, June.
    16. Zehetmayer Sonja & Graf Alexandra C. & Posch Martin, 2015. "Sample size reassessment for a two-stage design controlling the false discovery rate," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(5), pages 429-442, November.
    17. Karlis, Dimitris & Patilea, Valentin, 2007. "Confidence intervals of the hazard rate function for discrete distributions using mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5388-5401, July.
    18. Yacine Koucha & Alfredo D. Egidio dos Reis, 2021. "Approximations to ultimate ruin probabilities with a Wienner process perturbation," Papers 2107.02537, arXiv.org.
    19. Oba Shigeyuki & Ishii Shin, 2009. "Optimal Sufficient Statistics for Parametric and Non-Parametric Multiple Simultaneous Hypothesis Testing," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-27, June.
    20. Dickhaus Thorsten & Straßburger Klaus & Schunk Daniel & Morcillo-Suarez Carlos & Illig Thomas & Navarro Arcadi, 2012. "How to analyze many contingency tables simultaneously in genetic association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-33, July.
    21. Dimitri Karlis & Valentin Patilea, 2004. "Bootstrap Confidence Intervals in Mixtures of Discrete Distributions," Working Papers 2004-06, Center for Research in Economics and Statistics.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:35:y:2008:i:3:p:385-399. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.