Partial least squares for sparsely observed curves with measurement errors

03/25/2020

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by   Zhiyang Zhou, et al.

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Functional partial least squares (FPLS) is commonly used for fitting scalar-on-function regression models. For the sake of accuracy, FPLS demands that each realization of the functional predictor is recorded as densely as possible over the entire time span; however, this condition is sometimes violated in, e.g., longitudinal studies and missing data research. Targeting this point, we adapt FPLS to scenarios in which the number of measurements per subject is small and bounded from above. The resulting proposal is abbreviated as PLEASS. Under certain regularity conditions, we establish the consistency of estimators and give confidence intervals for scalar responses. Simulation studies help us test the accuracy and robustness of PLEASS. We finally apply PLEASS to clinical trial data and to medical imaging data.