Quasi-Monte Carlo for Highly Structured Generalised Response Models
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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.
KeywordsGeneralised linear mixed models High-dimensional integration Lattice rules Longitudinal data analysis Maximum likelihood Quasi-Monte Carlo Semiparametric regression Serial dependence Time series regression
AMS 2000 Subject Classification62J12 62M10 62M30 65D30 65D32
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