IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v10y2008i2d10.1007_s11009-007-9045-3.html
   My bibliography  Save this article

Quasi-Monte Carlo for Highly Structured Generalised Response Models

Author

Listed:
  • F. Y. Kuo

    (University of New South Wales)

  • W. T. M. Dunsmuir

    (University of New South Wales)

  • I. H. Sloan

    (University of New South Wales)

  • M. P. Wand

    (University of New South Wales)

  • R. S. Womersley

    (University of New South Wales)

Abstract

Highly structured generalised response models, such as generalised linear mixed models and generalised linear models for time series regression, have become an indispensable vehicle for data analysis and inference in many areas of application. However, their use in practice is hindered by high-dimensional intractable integrals. Quasi-Monte Carlo (QMC) is a dynamic research area in the general problem of high-dimensional numerical integration, although its potential for statistical applications is yet to be fully explored. We survey recent research in QMC, particularly lattice rules, and report on its application to highly structured generalised response models. New challenges for QMC are identified and new methodologies are developed. QMC methods are seen to provide significant improvements compared with ordinary Monte Carlo methods.

Suggested Citation

  • F. Y. Kuo & W. T. M. Dunsmuir & I. H. Sloan & M. P. Wand & R. S. Womersley, 2008. "Quasi-Monte Carlo for Highly Structured Generalised Response Models," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 239-275, June.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:2:d:10.1007_s11009-007-9045-3
    DOI: 10.1007/s11009-007-9045-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-007-9045-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-007-9045-3?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. Crainiceanu, Ciprian M. & Ruppert, David & Wand, Matthew P., 2005. "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i14).
    2. Pan, Jianxin & Thompson, Robin, 2007. "Quasi-Monte Carlo estimation in generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5765-5775, August.
    3. Jank, Wolfgang, 2005. "Quasi-Monte Carlo sampling to improve the efficiency of Monte Carlo EM," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 685-701, April.
    4. Gonzalez, Jorge & Tuerlinckx, Francis & De Boeck, Paul & Cools, Ronald, 2006. "Numerical integration in logistic-normal models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1535-1548, December.
    5. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    7. Brian S. Caffo & Wolfgang Jank & Galin L. Jones, 2005. "Ascent‐based Monte Carlo expectation– maximization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 235-251, April.
    8. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    9. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
    10. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    11. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    12. Pierre L’Ecuyer & Christiane Lemieux, 2002. "Recent Advances in Randomized Quasi-Monte Carlo Methods," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 419-474, Springer.
    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. Hejin Wang & Zhan Zheng, 2024. "Randomly Shifted Lattice Rules with Importance Sampling and Applications," Mathematics, MDPI, vol. 12(5), pages 1-20, 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. Basile, Roberto & Durbán, María & Mínguez, Román & María Montero, Jose & Mur, Jesús, 2014. "Modeling regional economic dynamics: Spatial dependence, spatial heterogeneity and nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 229-245.
    2. Hübler, Olaf, 2017. "Health and Body Mass Index: No Simple Relationship," IZA Discussion Papers 10620, Institute of Labor Economics (IZA).
    3. Lemmens, Aurélie & Croux, Christophe & Stremersch, Stefan, 2012. "Dynamics in the international market segmentation of new product growth," International Journal of Research in Marketing, Elsevier, vol. 29(1), pages 81-92.
    4. Chandra, Hukum & Salvati, Nicola & Chambers, Ray, 2018. "Small area estimation under a spatially non-linear model," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 19-38.
    5. Julie Vercelloni & M Julian Caley & Mohsen Kayal & Samantha Low-Choy & Kerrie Mengersen, 2014. "Understanding Uncertainties in Non-Linear Population Trajectories: A Bayesian Semi-Parametric Hierarchical Approach to Large-Scale Surveys of Coral Cover," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-9, November.
    6. Göran Kauermann & Mehboob Ali, 2021. "Semi-parametric regression when some (expensive) covariates are missing by design," Statistical Papers, Springer, vol. 62(4), pages 1675-1696, August.
    7. Takuma Yoshida, 2016. "Asymptotics and smoothing parameter selection for penalized spline regression with various loss functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 278-303, November.
    8. Michael Wegener & Göran Kauermann, 2017. "Forecasting in nonlinear univariate time series using penalized splines," Statistical Papers, Springer, vol. 58(3), pages 557-576, September.
    9. Lauren Hund & Jarvis T. Chen & Nancy Krieger & Brent A. Coull, 2012. "A Geostatistical Approach to Large-Scale Disease Mapping with Temporal Misalignment," Biometrics, The International Biometric Society, vol. 68(3), pages 849-858, September.
    10. Rachid Muleia & Makini Boothe & Osvaldo Loquiha & Marc Aerts & Christel Faes, 2020. "Spatial Distribution of HIV Prevalence among Young People in Mozambique," IJERPH, MDPI, vol. 17(3), pages 1-20, January.
    11. Lee, Wang-Sheng & McKinnish, Terra, 2019. "Locus of control and marital satisfaction: Couple perspectives using Australian data," Journal of Economic Psychology, Elsevier, vol. 74(C).
    12. Wood, Simon N., 2016. "Just Another Gibbs Additive Modeler: Interfacing JAGS and mgcv," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 75(i07).
    13. Veerabhadran Baladandayuthapani & Bani K. Mallick & Mee Young Hong & Joanne R. Lupton & Nancy D. Turner & Raymond J. Carroll, 2008. "Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogenesis," Biometrics, The International Biometric Society, vol. 64(1), pages 64-73, March.
    14. Chiara Bocci & Emilia Rocco, 2014. "Estimates for geographical domains through geoadditive models in presence of incomplete geographical information," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 283-305, June.
    15. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," LIDAM Discussion Papers ISBA 2013045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Hamdy F. F. Mahmoud & Inyoung Kim, 2023. "Semiparametric Integrated and Additive Spatio-Temporal Single-Index Models," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    17. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    18. Arthur Charpentier & Emmanuel Flachaire & Antoine Ly, 2017. "Econom\'etrie et Machine Learning," Papers 1708.06992, arXiv.org, revised Mar 2018.
    19. Hyunju Son & Youyi Fong, 2021. "Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    20. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.

    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:spr:metcap:v:10:y:2008:i:2:d:10.1007_s11009-007-9045-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.