Functional group bridge for simultaneous regression and support estimation
Functional group bridge for simultaneous regression and support estimation
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DOI：
10.1111/biom.13684
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发表时间：
2020-06
期刊：
影响因子：
1.9
通讯作者：
Zhengjia Wang;J. Magnotti;M. Beauchamp;Meng Li
中科院分区：
文献类型：
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作者：
Zhengjia Wang;J. Magnotti;M. Beauchamp;Meng Li
本文旨在研究颅内脑电图（iEEG）实验中不同实验条件下的脑活动差异。实验条件的对比效应在大多数区域通常为零，在某些局部区域为非零，从而产生局部稀疏函数。这样的研究本质上是一个函数-标量回归问题，人们的兴趣不仅集中在估计非参数函数上，而且集中在恢复函数支持上。我们提出了一种加权组桥方法，用于在函数-标量混合效应模型中同时进行函数估计和支持恢复，同时考虑函数数据中存在的异质性。利用B-样条函数将函数的稀疏性转化为维数增加的稀疏向量，提出了一种基于嵌套交替方向乘子法（ADMM）的快速非凸优化算法。建立了大样本特性。特别是，我们证明了估计的系数函数在L2范数下的极大极小意义下是速率最优的，并且类似于相变现象。对于支持度估计，我们在L∞$L_{\infty }$范数下得到了一个收敛速度，该收敛速度导致了δ-稀疏下的选择一致性，并利用一个简单的充分正则性条件得到了严格稀疏下的一个结果.提出了一种调整的扩展贝叶斯信息准则用于参数整定。所开发的方法说明通过模拟和应用程序的一个新的iEEG数据集研究多感官整合。
This paper is motivated by studying differential brain activities to multiple experimental condition presentations in intracranial electroencephalography (iEEG) experiments. Contrasting effects of experimental conditions are often zero in most regions and nonzero in some local regions, yielding locally sparse functions. Such studies are essentially a function‐on‐scalar regression problem, with interest being focused not only on estimating nonparametric functions but also on recovering the function supports. We propose a weighted group bridge approach for simultaneous function estimation and support recovery in function‐on‐scalar mixed effect models, while accounting for heterogeneity present in functional data. We use B‐splines to transform sparsity of functions to its sparse vector counterpart of increasing dimension, and propose a fast nonconvex optimization algorithm using nested alternative direction method of multipliers (ADMM) for estimation. Large sample properties are established. In particular, we show that the estimated coefficient functions are rate optimal in the minimax sense under the L2 norm and resemble a phase transition phenomenon. For support estimation, we derive a convergence rate under the L∞$L_{\infty }$ norm that leads to a selection consistency property under δ‐sparsity, and obtain a result under strict sparsity using a simple sufficient regularity condition. An adjusted extended Bayesian information criterion is proposed for parameter tuning. The developed method is illustrated through simulations and an application to a novel iEEG data set to study multisensory integration.