PENALIZED LIKELIHOOD FUNCTIONAL REGRESSION
PENALIZED LIKELIHOOD FUNCTIONAL REGRESSION
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DOI：
10.5705/ss.2012.235
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发表时间：
2014-04-01
影响因子：
1.4
通讯作者：
Wang, Xiao
中科院分区：
文献类型：
--
作者：
Du, Pang;Wang, Xiao
本文研究了具有标量响应和函数预测的广义泛函线性模型。给定函数预测量的响应假定来自指数族的分布。提出了一种惩罚似然方法来估计模型中的未知截距和系数函数。推导了系数函数的逐点置信区间和预测区间等推理工具。建立了预测平均响应误差的极小极大收敛速度。它表明，惩罚似然估计达到最佳的收敛速度。我们的模拟表明，对现有的方法的竞争力的表现。该方法进一步说明了在使用DTI纤维束成像区分胼胝体束与多发性硬化症正常束。
This paper studies the generalized functional linear model with a scalar response and a functional predictor. The response given the functional predictor is assumed to come from the distribution of an exponential family. A penalized likelihood approach is proposed to estimate the unknown intercept and coefficient function in the model. Inference tools such as point-wise confidence intervals of the coefficient function and prediction intervals are derived. The minimax rate of convergence for the error in predicting the mean response is established. It is shown that the penalized likelihood estimator attains the optimal rate of convergence. Our simulations demonstrate a competitive performance against the existing approach. The method is further illustrated in the use of the DTI tractography to distinguish corpus callosum tracts with multiple sclerosis from normal tracts.