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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
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    References listed on IDEAS

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    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.

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