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Abstract:
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We propose a new methodology, called AFSSEN, to simultaneously select important variables and produce smooth estimates of their parameters in a function-on-scalar linear model with sub-Gaussian errors and high-dimensional predictors. In our model, the data live in a general real separable Hilbert space, H, but an arbitrary linear operator of the parameters are enforced to lie in an RKHS, K, so that the parameter estimates inherit properties from the RKHS kernel, such as smoothness and periodicity. We use a regularization method that exploits an adaptive Elastic Net penalty where the L1 and L2 norms are introduced in H and K respectively. Using two norms we are able to better control both smoothing and variable selection. AFFSEN is illustrated via a simulation study and microbiome data using a very fast algorithm for computing the estimators based on a functional coordinate descent whose interface is written in R, but with the backend written in C++.
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