Motivated by analyzing two large-scale real functional data sets, we propose an optimal
subsampling method based on the functional L-optimality criterion and further extend the proposed functional L-optimality subsampling (FLoS) method to the functional generalized linear model to cope with the scenario of the response being a discrete or categorical variable. We establish the asymptotic properties of the FLoS estimators. The finite sample performance of our proposed FLoS method is investigated by extensive simulation studies. The FLoS method is further demonstrated by analyzing two large-scale real data sets: global climate data and the kidney transplant data. The analysis results on these data show that the FLoS method is much better than the uniform subsampling approach and can well approximate the results based on the full data while dramatically reducing the computation time and memory.
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