We develop a novel approach for estimating a high-dimensional and non- parametric graphical model for functional data. Our approach is built on a new linear operator, the functional additive partial correlation operator, which extends the partial correlation matrix to both the nonparametric and functional setting. We show that its nonzero elements can be used to characterize the graph, and we employ sparse regression techniques for graph estimation. Moreover, the method does not rely on any distributional assumptions and does not require the computation of multi-dimensional kernels, thus it avoids the curse of dimensionality. We establish both estimation con- sistency and graph selection consistency of the proposed estimator, while allowing the number of nodes to grow with the increasing sample size. Through simulation studies, we demonstrate that our method performs better than existing methods in cases where the Gaussian or Gaussian copula assumption does not hold. We also demonstrate the performance of the proposed method by study of an electroencephalography dataset to construct a brain network.
Joint work with Kuang-Yao Lee, Temple University, Philadelphia, USA and Bing Li, Pennsylvania State University, University Park, USA
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