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Abstract:
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This paper develops a method for collective estimation of spectral density functions (SDFs) for time series and spatial data. Due to the similarities among the SDFs, the log-SDF can be represented using a common set of basis functions. The basis shared by the collection of the log-SDFs is estimated as a low-dimensional manifold of a large space spanned by a pre-specified rich basis. Collective estimation approach allows pooling information and borrowing strength across SDFs to achieve better estimation efficiency. Moreover, each estimated spectral density has a concise representation using the coefficients of the basis expansion and these coefficients can be used for visualization, clustering, and classification purposes. Penalized Whittle pseudo-maximum likelihood approach is used to fit the model and a modified blockwise Newton-type algorithm is developed for computation. The performance of SDF estimation and clustering is examined by simulation studies. Finally, we illustrate the proposed methods using multi-site time series data for one-dimensional SDFs, and extend to two-dimensional SDFs for spatial data, taking the spatial dependence into account.
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