论文标题

在真实发现比例上同时置信度界限平滑的差异

Localizing differences in smooths with simultaneous confidence bounds on the true discovery proportion

论文作者

Swanson, David

论文摘要

我们演示了一种定位的方法,其中两个样条术语或平滑的方法使用基于真正的发现比例(TDP)解释有所不同。该过程对两种平滑段之间存在真正差异的某些区域的比例产生了陈述,这是由于使用假设检验对基础系数的收集进行参数化平滑词的收集而产生的。该方法避免了否则临时手段做出这样的陈述,例如子集数据,然后对截短的样条项进行假设检验。 TDP估计是同时限制的1-α置信度。这意味着,无论估计TDP的区域数量如何,在该地区的实际差异或真实发现的比例中,TDP的估计值是实际差异或真实发现的比例。我们的过程基于使用模拟本地测试的封闭测试。该本地测试要求该方法基础的“多变量CHI-SQ测试统计量”是基于子集的正回归(PRDS),我们显示。该方法的驱动力很大,因为结果是二级或更少的惩罚B-Spline的协方差矩阵的偏离衰减结构。我们证明了在模拟中实现估计的TDP,并分析了脑瘫患者步行步态的研究。

We demonstrate a method for localizing where two spline terms, or smooths, differ using a true discovery proportion (TDP) based interpretation. The procedure yields a statement on the proportion of some region where true differences exist between two smooths, which results from use of hypothesis tests on collections of basis coefficients parameterizing the smooths. The methodology avoids otherwise ad hoc means of making such statements like subsetting the data and then performing hypothesis tests on the truncated spline terms. TDP estimates are 1-alpha confidence bounded simultaneously. This means that the TDP estimate for a region is a lower bound on the proportion of actual difference, or true discoveries, in that region with high confidence regardless of the number of regions at which TDP is estimated. Our procedure is based on closed-testing using Simes local test. This local test requires that the `multivariate chi-sq test statistics of generalized Wishart type' underlying the method are positive regression dependent on subsets (PRDS), which we show. The method is well-powered because of a result on the off-diagonal decay structure of the covariance matrix of penalized B-splines of degree two or fewer. We demonstrate achievement of estimated TDP in simulation and analyze a study of walking gait of cerebral palsy patients.

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