基于真实发现比例的同时置信界定位光滑函数的差异
Localizing differences in smooths with simultaneous confidence bounds on the true discovery proportion
AI总结：
本研究提出一种基于真实发现比例（TDP）同时置信界的方法，通过Simes局部检验的闭合检验定位两个光滑函数的差异区域，证明了相关统计量的PRDS性质，借助低次惩罚B样条协方差的非对角衰减结构实现良好功效，经仿真和脑瘫步态研究验证有效。
摘要：
我们提出了一种基于真实发现比例（TDP）解释的方法，用于定位两个样条项（即光滑函数）存在差异的位置。该过程通过对参数化光滑函数的基系数集合进行假设检验，得出关于两个光滑函数间存在真实差异的区域比例的结论。该方法避免了此类分析中常用的临时手段，例如先对数据取子集再对截断样条项执行假设检验。TDP估计值具有1-α的同时置信下界，这意味着无论估计TDP的区域数量有多少，某一区域的TDP估计值都是该区域内真实差异（即真实发现）比例的高置信度下界。我们的方法基于采用Simes局部检验的闭合检验法。该局部检验要求方法底层的“广义Wishart型多元卡方检验统计量”在子集上满足正回归依赖（PRDS）性质，我们证明了这一性质。由于二次及以下惩罚B样条的协方差矩阵具有非对角元衰减结构，该方法具备良好的统计功效。我们通过仿真实验验证了TDP估计的有效性，并对一项脑瘫患者行走步态的研究进行了分析。
英文摘要：
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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