This article is motivated by studying multisensory effects on brain activities in intracranial electroencephalography (iEEG) experiments. Differential brain activities to multisensory stimulus presentations are zero in most regions and non-zero 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 non-convex 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 $L_2$ norm and resemble a phase transition phenomenon. For support estimation, we derive a convergence rate under the $L_{\infty}$ norm that leads to a sparsistency property under $\delta$-sparsity, and provide a simple sufficient regularity condition under which a strict sparsistency property is established. An adjusted extended Bayesian information criterion is proposed for parameter tuning. The developed method is illustrated through simulation and an application to a novel iEEG dataset to study multisensory integration. We integrate the proposed method into RAVE, an R package that gains increasing popularity in the iEEG community.
翻译:文章的动因是研究大脑在内部电子感官学(iEEG)实验中对大脑活动的多重感知影响。 不同大脑活动在多感性刺激演示中在大多数区域为零,在一些地方区域为非零,产生本地稀疏的功能。 这些研究基本上是一个功能性局部回归问题, 兴趣不仅集中在估算非对称功能上, 也集中在恢复功能支持。 我们提议了一种加权群体连接法, 用于同时估算功能, 支持功能- 天际混合效应模型的恢复, 同时计算功能数据中的异质性。 我们使用 B- Spline 将功能的宽度转换成其稀薄的矢量对应的增强维度, 并提议一种快速非对齐优化的算法, 使用嵌套替代的乘以乘积的乘数法(ADMMM) 进行估算。 特别是, 我们表明,根据 $L_ 2 标准估算的微量值值值, 和 阶段过渡现象。 为了支持估算, 我们根据 $- Indality a clodiversive rodutional ruditional roditional deal deal deality a dal deal deal dealtistration, 在 rodistration a roduce a made deal deal deal deal deal deal deceal deal deal deal deal deal deal deal deal deal a rod a rodistritaltistration a rodistrit. a rod a a a rotistritaltald a rod a roticealticeild rod a rod a rod a rod rod a a rod a rod a rodaldaldaldaldaldaldald a rod a rod a rodald a roddaldald a rod a rod a rod rod a rod a rod rod a rod rod a rodal de rodaldald a rodaldaldaldald a rod rod a rod a