## Bernoulli

• Bernoulli
• Volume 13, Number 4 (2007), 1179-1194.

### The delta method for analytic functions of random operators with application to functional data

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 13, Number 4 (2007), 1179-1194.

Dates
First available in Project Euclid: 9 November 2007

https://projecteuclid.org/euclid.bj/1194625607

Digital Object Identifier
doi:10.3150/07-BEJ6180

Mathematical Reviews number (MathSciNet)
MR2364231

Zentralblatt MATH identifier
1129.62011

#### Citation

Cupidon, J.; Gilliam, D.S.; Eubank, R.; Ruymgaart, F. The delta method for analytic functions of random operators with application to functional data. Bernoulli 13 (2007), no. 4, 1179--1194. doi:10.3150/07-BEJ6180. https://projecteuclid.org/euclid.bj/1194625607

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