IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v23y2011i2p513-531.html
   My bibliography  Save this article

Smooth density estimation with moment constraints using mixture distributions

Author

Listed:
  • Ani Eloyan
  • Sujit Ghosh

Abstract

Statistical analysis often involves the estimation of a probability density based on a sample of observations. A commonly used nonparametric method for solving this problem is the kernel-based method. The motivation is that any continuous density can be approximated by a mixture of densities with appropriately chosen bandwidths. In many practical applications, we may have specific information about the moments of the density. A nonparametric method using a mixture of known densities is proposed that conserves a given set of moments. A modified expectation–maximisation algorithm for estimating the weights of the mixture density is then developed. The proposed method also obtains an estimate of the number of components in the mixture needed for optimal approximation. The proposed method is compared with two popular density estimation methods using simulated data and it is shown that the proposed estimate outperforms the others. The method is then illustrated by applying it to several real-data examples.

Suggested Citation

  • Ani Eloyan & Sujit Ghosh, 2011. "Smooth density estimation with moment constraints using mixture distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 513-531.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:513-531
    DOI: 10.1080/10485252.2010.532554
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2010.532554
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2010.532554?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wendimagegn Ghidey & Emmanuel Lesaffre & Paul Eilers, 2004. "Smooth Random Effects Distribution in a Linear Mixed Model," Biometrics, The International Biometric Society, vol. 60(4), pages 945-953, December.
    2. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    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. Bao, Junshu & Hanson, Timothy E., 2016. "A mean-constrained finite mixture of normals model," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 93-99.
    2. Kun Meng & Ani Eloyan, 2021. "Principal manifold estimation via model complexity selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 369-394, April.
    3. Eloyan, Ani & Ghosh, Sujit K., 2013. "A semiparametric approach to source separation using independent component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 383-396.
    4. Kuangyu Wen & Ximing Wu & David J. Leatham, 2021. "Spatially Smoothed Kernel Densities with Application to Crop Yield Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 349-366, September.

    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. Ho, Remus K.W. & Hu, Inchi, 2008. "Flexible modelling of random effects in linear mixed models--A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1347-1361, January.
    2. Shuang Zhang & Xingdong Feng, 2022. "Distributed identification of heterogeneous treatment effects," Computational Statistics, Springer, vol. 37(1), pages 57-89, March.
    3. Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.
    4. Peng Zhang & Peter X.-K. Song & Annie Qu & Tom Greene, 2008. "Efficient Estimation for Patient-Specific Rates of Disease Progression Using Nonnormal Linear Mixed Models," Biometrics, The International Biometric Society, vol. 64(1), pages 29-38, March.
    5. N. T. Longford & Pierpaolo D'Urso, 2011. "Mixture models with an improper component," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2511-2521, January.
    6. Conti, Gabriella & Frühwirth-Schnatter, Sylvia & Heckman, James J. & Piatek, Rémi, 2014. "Bayesian exploratory factor analysis," Journal of Econometrics, Elsevier, vol. 183(1), pages 31-57.
    7. Zhengyi Zhou & David S. Matteson & Dawn B. Woodard & Shane G. Henderson & Athanasios C. Micheas, 2015. "A Spatio-Temporal Point Process Model for Ambulance Demand," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 6-15, March.
    8. Peter Hall & Tapabrata Maiti, 2009. "Deconvolution methods for non‐parametric inference in two‐level mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 703-718, June.
    9. Francisco Richter & Bart Haegeman & Rampal S. Etienne & Ernst C. Wit, 2020. "Introducing a general class of species diversification models for phylogenetic trees," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 261-274, August.
    10. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    11. Nalini Ravishanker & Dipak K. Dey, 2000. "Multivariate Survival Models with a Mixture of Positive Stable Frailties," Methodology and Computing in Applied Probability, Springer, vol. 2(3), pages 293-308, September.
    12. Yasutomo Murasawa, 2020. "Measuring public inflation perceptions and expectations in the UK," Empirical Economics, Springer, vol. 59(1), pages 315-344, July.
    13. Minjung Kyung & Ju-Hyun Park & Ji Yeh Choi, 2022. "Bayesian Mixture Model of Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 946-966, September.
    14. Luigi Spezia, 2019. "Modelling covariance matrices by the trigonometric separation strategy with application to hidden Markov models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 399-422, June.
    15. Michael E. Sobel & Bengt Muthén, 2012. "Compliance Mixture Modelling with a Zero-Effect Complier Class and Missing Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1037-1045, December.
    16. Rosychuk, Rhonda J. & Shofiqul Islam, 2009. "Parameter estimation in a model for misclassified Markov data -- a Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3805-3816, September.
    17. Hlouskova, Jaroslava & Sögner, Leopold, 2020. "GMM estimation of affine term structure models," Econometrics and Statistics, Elsevier, vol. 13(C), pages 2-15.
    18. Yuan Fang & Dimitris Karlis & Sanjeena Subedi, 2022. "Infinite Mixtures of Multivariate Normal-Inverse Gaussian Distributions for Clustering of Skewed Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 510-552, November.
    19. Kazuhiko Kakamu, 2022. "Bayesian analysis of mixtures of lognormal distribution with an unknown number of components from grouped data," Papers 2210.05115, arXiv.org, revised Sep 2023.
    20. Hwan Chung & Brian P. Flaherty & Joseph L. Schafer, 2006. "Latent class logistic regression: application to marijuana use and attitudes among high school seniors," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 723-743, October.

    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:taf:gnstxx:v:23:y:2011:i:2:p:513-531. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.