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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. 

We propose time‐varying coefficient model selection and estimation based on the spline approach, which is capable of capturing time‐dependent covariate effects. The new penalty function utilizes local‐region information for varying‐coefficient estimation, in contrast to the traditional model selection approach focusing on the entire region. The proposed method is extremely useful when the signals associated with relevant predictors are time‐dependent, and detecting relevant covariate effects in the local region is more scientifically relevant than those of the entire region. Our simulation studies indicate that the proposed model selection incorporating local features outperforms the global feature model selection approaches. The proposed method is also illustrated through a longitudinal growth and health study from National Heart, Lung, and Blood Institute.

 

Nonparametric model-assisted estimators have been proposed to improve estimates of finite population parameters. Flexible nonparametric models provide more reliable estimators when a parametric model is misspecified. In this article, we propose an information criterion to select appropriate auxiliary variables to use in an additive model-assisted method. We approximate the additive nonparametric components using polynomial splines and extend the Bayesian Information Criterion (BIC) for finite populations. By removing irrelevant auxiliary variables, our method reduces model complexity and decreases estimator variance. We establish that the proposed BIC is asymptotically consistent in selecting the important explanatory variables when the true model is additive without interactions, a result supported by our numerical study. Our proposed method is easier to implement and better justified theoretically than the existing method proposed in the literature.