Oracle-efficient estimation for functional data error distribution with simultaneous confidence band
Oracle-efficient estimation for functional data error distribution with simultaneous confidence band
复制标题
使用同步置信带对功能数据误差分布进行 Oracle 高效估计
DOI：
10.1016/j.csda.2021.107363
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发表时间：
2021-10-07
影响因子：
1.8
通讯作者：
Yang, Lijian
中科院分区：
文献类型：
--
作者：
Wang, Jiangyan;Gu, Lijie;Yang, Lijian
基于核分布估计（KDE），构造了稠密函数型数据误差分布的Kolmogorov-Smirnov（K-S）联合置信带（SCB）. KDE是从较少数量的测量上的B样条轨迹的残差计算的，而B样条轨迹是从剩余的较大测量集合计算的。在温和和简单的假设下，证明了KDE是误差分布的一致预言有效估计，并且SCB具有与基于不可观测误差的经验累积分布函数（EDF）的经典K-S SCB相同的渐近性质.仿真实例证实了理论研究结果。最后以EEG（Electroencephalograph）数据和股票数据为例说明了该方法的有效性. (C)2021爱思唯尔有限公司版权所有。
Kolmogorov-Smirnov (K-S) simultaneous confidence band (SCB) is constructed for the error distribution of dense functional data based on kernel distribution estimator (KDE). The KDE is computed from residuals of B spline trajectories over a smaller number of measurements, whereas the B spline trajectories are computed from the remaining larger set of measurements. Under mild and simple assumptions, it is shown that the KDE is a uniformly oracle-efficient estimator of the error distribution, and the SCB has the same asymptotic properties as the classic K-S SCB based on the infeasible empirical cumulative distribution function (EDF) of unobserved errors. Simulation examples corroborate with the theoretical findings. The proposed method is illustrated by examples of an EEG (Electroencephalogram) data and a stock data. (C) 2021 Elsevier B.V. All rights reserved.