论文标题
功能性增量残差和对基于力矩统计的同时置信带的应用
Functional delta residuals and applications to simultaneous confidence bands of moment based statistics
论文作者
论文摘要
给定估计器和参数转换的功能性中心极限（FCLT），我们构建了随机过程，称为功能增量残差，该过程渐近地具有与功能三角洲方法的极限过程相同的协方差结构。这些残差的明确结构证明了这些残差，用于基于力矩的估计器的转换和用于生成功能性增量残差的乘数bootstrap FCLT。后者用于始终估计功能增量方法的极限过程的最大值的分位数，以便为转换的功能参数构造渐近有效的同时置信带。在模拟中说明了开发结构的覆盖率的性能，应用于Cohen的D，偏度和峰度的功能版本，并讨论了它们测试高斯性的应用。
Given a functional central limit (fCLT) for an estimator and a parameter transformation, we construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the limit process of the functional delta method. An explicit construction of these residuals for transformations of moment-based estimators and a multiplier bootstrap fCLT for the resulting functional delta residuals are proven. The latter is used to consistently estimate the quantiles of the maximum of the limit process of the functional delta method in order to construct asymptotically valid simultaneous confidence bands for the transformed functional parameters. Performance of the coverage rate of the developed construction, applied to functional versions of Cohen's d, skewness and kurtosis, is illustrated in simulations and their application to test Gaussianity is discussed.
