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Semiparametric models and inference for biomedical time series with extra-variation. (English) Zbl 1097.62561
Summary: Biomedical trials often give rise to data having the form of time series of a common process on separate individuals. One model, which has been proposed to explain variations in such series across individuals, is a random effects model based on sample periodograms. The use of spectral coefficients enables models for individual series to be constructed on the basis of standard asymptotic theory, whilst variations between individuals are handled by permitting a random effect perturbation of model coefficients.
This paper extends such methodology in two ways: first, by enabling a nonparametric specification of underlying spectral behaviour; second, by addressing some of the tricky computational issues which are encountered when working with this class of random effect models. This leads to a model in which a population spectrum is specified nonparametrically through a dynamic system, and the processes measured on individuals within the population are assumed to have a spectrum which has a random effect perturbation from the population norm. Simulation studies show that standard MCMC algorithms give effective inferences for this model, and applications to biomedical data suggest that the model itself is capable of revealing scientifically important structure in temporal characteristics both within and between individual processes.

MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
62M15 Inference from stochastic processes and spectral analysis
62G08 Nonparametric regression and quantile regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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