The completion of covariance kernels

DOI10.1214/22-AOS2228MaRDI QIDQ2112811

Kartik G. Waghmare, Victor M. Panaretos

Publication date: 12 January 2023

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.07350

zbMATH Keywords

inverse problemidentifiabilityfunctional data analysisgraphical modelfragmentspositive-definite continuation

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Nonparametric estimation (62G05) Linear operator methods in interpolation, moment and extension problems (47A57) Inverse problems for integral equations (45Q05) Matrix completion problems (15A83) Probabilistic graphical models (62H22)

Uses Software

• R
• fdapace
• GitHub
• covcomp

Cites Work

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• Theory of reproducing kernels and applications
• Positive definite completions of partial Hermitian matrices
• Schur products and matrix completions
• Extensions of band matrices with band inverses
• Positive definite functions and generalizations, an historical survey
• Functional data analysis by matrix completion
• On the optimal reconstruction of partially observed functional data
• Continuation of Hermitian positive definite functions and related questions
• The extension problem for positive-definite functions
• Joint Measures and Cross-Covariance Operators
• Basis expansions for functional snippets
• Components and Completion of Partially Observed Functional Data
• Approximating fragmented functional data by segments of Markov chains
• Recovering covariance from functional fragments
• The characterization problem for isotropic covariance functions
• Estimating the Covariance of Fragmented and Other Related Types of Functional Data

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