Hypothesis testing in functional linear models.
Hypothesis testing in functional linear models.
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作者：
Su YR;Di CZ;Hsu L
功能数据经常出现在生物医学研究中，其中研究功能预测因子和标量响应变量之间的关系通常很有趣。虽然功能线性模型（FLM）被广泛用于解决这些问题，但在FLM框架中对功能关联的假设检验仍然具有挑战性。测试功能效应的常用方法是通过功能主成分（PC）分析进行降维。然而，其功耗性能取决于pc数量的选择，并没有系统的研究。在本文中，我们首先研究了不同阈值的wald型检验在选择函数协变量的pc数时的功率性能，并表明功率对阈值的选择很敏感。为了解决这个问题，我们提出了一种新的排序和选择主成分的方法来构造检验统计量。所提出的方法既考虑了与响应的关联，又考虑了沿每个特征函数的变化。我们建立了它的理论性质，并通过模拟评估了它的有限样本性质。仿真结果表明，本文提出的测试方法对阈值的选择具有更强的鲁棒性，并且与现有方法一样强大，甚至比现有方法更强大。然后，我们将所提出的方法应用于从扩散张量成像神经束研究中获得的脑白质束数据。
Functional data arise frequently in biomedical studies, where it is often of interest to investigate the association between functional predictors and a scalar response variable. While functional linear models (FLM) are widely used to address these questions, hypothesis testing for the functional association in the FLM framework remains challenging. A popular approach to testing the functional effects is through dimension reduction by functional principal component (PC) analysis. However, its power performance depends on the choice of the number of PCs, and is not systematically studied. In this paper, we first investigate the power performance of the Wald-type test with varying thresholds in selecting the number of PCs for the functional covariates, and show that the power is sensitive to the choice of thresholds. To circumvent the issue, we propose a new method of ordering and selecting principal components to construct test statistics. The proposed method takes into account both the association with the response and the variation along each eigenfunction. We establish its theoretical properties and assess the finite sample properties through simulations. Our simulation results show that the proposed test is more robust against the choice of threshold while being as powerful as, and often more powerful than, the existing method. We then apply the proposed method to the cerebral white matter tracts data obtained from a diffusion tensor imaging tractography study.
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影响因子：
3.7
作者：
Crainiceanu CM;Staicu AM;Di CZ
通讯作者：
Di CZ
DOI：
10.1111/rssb.12036
发表时间：
2014-06-01
期刊：
Journal of the Royal Statistical Society. Series B, Statistical methodology
影响因子：
--
作者：
Zhu H;Yao F;Zhang HH
通讯作者：
Zhang HH
影响因子：
4.5
作者：
Yao, F;Müller, HG;Wang, JL
通讯作者：
Wang, JL
影响因子：
0.8
作者：
Cardot, H;Ferraty, F;Sarda, P
通讯作者：
Sarda, P
影响因子：
1
作者：
Cardot, H;Ferraty, F;Sarda, P
通讯作者：
Sarda, P