摘要翻译：
本文导出了正则泛函正则相关估计量的渐近分布和总体变量的渐近分布。该方法是基于将这些正则化量表示为相关的正则化算子对的最大特征值和相应的本征函数的可能性，类似于欧几里德情况。已知样本协方差算子的弱收敛性，结合协方差算子解析函数的delta方法，得到了相关算子对的弱收敛性。从后者的弱收敛性出发，借助于进一步的摄动理论，可以导出所关注的正则量的极限分布。
---
英文标题：
《The delta method for analytic functions of random operators with
  application to functional data》
---
作者：
J. Cupidon, D.S. Gilliam, R. Eubank, F. Ruymgaart
---
最新提交年份：
2007
---
分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

---
英文摘要：
  In this paper, the asymptotic distributions of estimators for the regularized functional canonical correlation and variates of the population are derived. The method is based on the possibility of expressing these regularized quantities as the maximum eigenvalue and the corresponding eigenfunctions of an associated pair of regularized operators, similar to the Euclidean case. The known weak convergence of the sample covariance operator, coupled with a delta-method for analytic functions of covariance operators, yields the weak convergence of the pair of associated operators. From the latter weak convergence, the limiting distributions of the canonical quantities of interest can be derived with the help of some further perturbation theory.
---
PDF链接：
https://arxiv.org/pdf/711.4368