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Abstract:
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Historical Functional Linear Models (HFLM) quantify associations between a functional predictor and functional outcome where the predictor is an exposure variable occurring before, or concurrently with, the outcome. Prior work on the HFLM has largely focused on estimation using frequentist methods, with little attention paid to formal inference or adjustment for multiple testing. We propose a new functional regression model that estimates the time-varying, lagged association between a functional outcome and a functional exposure. Building upon recently developed function-on-function regression methods, the model employs a novel wavelet packet decomposition of both functions that allows us to strictly enforce the temporal ordering of exposure and outcome, which is not possible with existing wavelet-based functional models. Using a fully Bayesian approach, we conduct formal inference on the time-varying lagged association, while adjusting for multiple testing. We investigate our method and inference procedures in simulation and analyze data on the impact of lagged exposure to particulate matter finer than 2.5?g on heart rate variability in a cohort of journeyman boilermakers.
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