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Smooth and locally sparse estimation for multiple-output functional linear regression. (English) Zbl 07194289
Summary: Functional data analysis has attracted substantial research interest and the goal of functional sparsity is to produce a sparse estimate which assigns zero values over regions where the true underlying function is zero, i.e. no relationship between the response variable and the predictor variable. In this paper, we consider a functional linear regression model that explicitly incorporates the interconnections among the responses. We propose a locally sparse (i.e. zero on some subregions) estimator, multiple-smooth and locally sparse (m-SLoS) estimator, for coefficient functions base on the interconnections among the responses. Simulations show excellent numerical performance of the proposed method in terms of the estimation of coefficient functions especially the coefficient functions are same for all multivariate responses. Practical merit of this modelling is demonstrated by one real application and the prediction shows significant improvements.
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