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

DOI10.3150/07-BEJ6180zbMath1129.62011arXiv0711.4368MaRDI QIDQ2469671

Yanyan Li

Publication date: 6 February 2008

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.4368

zbMATH Keywords

weak convergenceperturbation theoryregularization of operatorsdelta-method for analytic functions of covariance operatorsregularized functional canonical correlation and variates

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Measures of association (correlation, canonical correlation, etc.) (62H20) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (15)

Optimal-order bounds on the rate of convergence to normality in the multivariate delta method ⋮ Robust smoothed canonical correlation analysis for functional data ⋮ A history of the delta method and some new results ⋮ Functional linear regression via canonical analysis ⋮ Application of a delta-method for random operators to testing equality of two covariance operators ⋮ A note on random perturbations of a multiple eigenvalue of a Hermitian operator ⋮ Robust sieve estimators for functional canonical correlation analysis ⋮ Canonical correlation analysis for irregularly and sparsely observed functional data ⋮ Inferential procedures for partially observed functional data ⋮ High-dimensional principal projections ⋮ The optimal rate of canonical correlation analysis for stochastic processes ⋮ The Fréchet derivative of an analytic function of a bounded operator with some applications ⋮ Some asymptotic theory for functional regression and classification ⋮ Two sample inference in functional linear models ⋮ Functional partial canonical correlation

Cites Work

• Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
• Some properties of canonical correlations and variates in infinite dimensions
• Canonical correlation for stochastic processes
• The Fréchet derivative of an analytic function of a bounded operator with some applications
• Some applications of Watson's perturbation approach to random matrices
• Methods of canonical analysis for functional data.
• Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations
• Penalized discriminant analysis
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