Global Inference and Test for Eigensystems of Imaging Data Over Complicated Domains
提出一种基于双变量样条的非参数方法，用于分析复杂域上图像数据的特征系统，估计量具有渐近最优性和计算效率，支持置信区间、同时置信带及两样本检验，并通过海水温度数据验证。
A nonparametric approach for analyzing eigensystems of image data over a complex domain is novelly developed. The proposed estimators, which are based on bivariate splines, have both oracle efficiency of Op(n−1/2), meaning they are asymptotically indistinguishable from estimators computed with true trajectories, and computational efficiency with more convenient spectrum decomposition forms. Under mild conditions, we derive consistency and weak convergence of our proposed estimators, which can be used to construct confidence intervals and simultaneous confidence corridors for any individual eigenvalue and eigenfunction, as well as design uniform inference procedures for eigensystems with a diverging number of components. In addition, we extend our method to two-sample test problems. Extensive simulation results provide strong support for the asymptotic theory, and the procedures are applied to two potential seawater temperature data sets to demonstrate its validity.