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My dissertation presents a novel statistical method to estimate a sparse signal in functional data and to construct confidence bands for the signal. Existing methods for inference for the mean function in this framework include smoothing splines and kernel estimates. Our methodology involves thresholding a least squares estimator, and the threshold level depends on the sources of variability that exist in this type of data. The proposed estimation method and the confidence bands successfully adapt to the sparsity of the signal. We present supporting evidence through simulations and applications to real datasets.
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