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Spatial–temporal data arise frequently in biomedical, environmental, political and social science studies. Capturing dynamic changes of time-varying correlation structure is scientifically important in spatio-temporal data analysis. We approximate the time-varying empirical estimator of the spatial correlation matrix by groups of selected basis matrices representing substructures of the correlation matrix. After projecting the correlation structure matrix onto a space spanned by basis matrices, we also incorporate varying-coefficient model selection and estimation for signals associated with relevant basis matrices. The unique feature of the proposed method is that signals at local regions corresponding with time can be identified through the proposed penalized objective function. Theoretically, we show model selection consistency and the oracle property in detecting local signals for the varying-coefficient estimators. The proposed method is illustrated through simulation studies and brain fMRI data.
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TIME-VARYING ESTIMATION AND DYNAMIC MODEL SELECTION WITH AN APPLICATION OF NETWORK DATA
In many biomedical and social science studies, it is important to identify and predict the dynamic changes of associations among network data over time. We propose a varying-coefficient model to incorporate time-varying network data, and impose a piecewise penalty function to capture local features of the network associations. The proposed approach is semi-parametric, and therefore flexible in modeling dynamic changes of association in network data problems. Furthermore, the approach can identify the time regions when dynamic changes of associations occur. To achieve a sparse network estimation at local time intervals, we implement a group penalization strategy involving parameters that overlap between groups. However, this makes the optimization process challenging for large-dimensional network data observed at many time points. We develop a fast algorithm, based on the smoothing proximal-gradient method, that is computationally efficient and accurate. We illustrate the proposed method through simulation studies and children's attention deficit hyperactivity disorder fMRI data, showing that the proposed method and algorithm recover dynamic network changes over time efficiently.
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- Award ID(s):
- 1812258
- PAR ID:
- 10148932
- Date Published:
- Journal Name:
- Statistica sinica
- Volume:
- 30
- ISSN:
- 1996-8507
- Page Range / eLocation ID:
- 251-284
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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