scholarly journals Fast covariance estimation for high-dimensional functional data

2014 ◽  
Vol 26 (1-2) ◽  
pp. 409-421 ◽  
Author(s):  
Luo Xiao ◽  
Vadim Zipunnikov ◽  
David Ruppert ◽  
Ciprian Crainiceanu
Keyword(s):  
Functional Data ◽  
Covariance Estimation ◽  
High Dimensional

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

scholarly journals Smoothed Linear Modeling for Smooth Spectral Data

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Douglas M. Hawkins ◽  
Edgard M. Maboudou-Tchao
Keyword(s):  
Spectral Data ◽  
Functional Data ◽  
High Dimensional Data ◽  
Basis Functions ◽  
High Dimensional ◽  
Data Sets ◽  
Linear Modeling ◽  
Linear Discriminant ◽  
Smooth Basis ◽  
Prediction Problems

Classification and prediction problems using spectral data lead to high-dimensional data sets. Spectral data are, however, different from most other high-dimensional data sets in that information usually varies smoothly with wavelength, suggesting that fitted models should also vary smoothly with wavelength. Functional data analysis, widely used in the analysis of spectral data, meets this objective by changing perspective from the raw spectra to approximations using smooth basis functions. This paper explores linear regression and linear discriminant analysis fitted directly to the spectral data, imposing penalties on the values and roughness of the fitted coefficients, and shows by example that this can lead to better fits than existing standard methodologies.

scholarly journals Smoothing and Mean–Covariance Estimation of Functional Data with a Bayesian Hierarchical Model

2016 ◽  
Vol 11 (3) ◽  
pp. 649-670 ◽  
Author(s):  
Jingjing Yang ◽  
Hongxiao Zhu ◽  
Taeryon Choi ◽  
Dennis D. Cox
Keyword(s):  
Hierarchical Model ◽  
Functional Data ◽  
Bayesian Hierarchical Model ◽  
Covariance Estimation ◽  
Bayesian Hierarchical

scholarly journals High-dimensional covariance estimation under the presence of outliers

2016 ◽  
Vol 9 (4) ◽  
pp. 461-468
Author(s):  
Hsin-Cheng Huang ◽  
Thomas C. M. Lee
Keyword(s):  
Covariance Estimation ◽  
High Dimensional

scholarly journals High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence

2011 ◽  
Vol 5 (0) ◽  
pp. 935-980 ◽  
Author(s):  
Pradeep Ravikumar ◽  
Martin J. Wainwright ◽  
Garvesh Raskutti ◽  
Bin Yu
Keyword(s):  
Covariance Estimation ◽  
High Dimensional

Editorial for the special issue on High-dimensional and functional data analysis

2019 ◽  
Vol 131 ◽  
pp. 10-11
Author(s):  
Frederic Ferraty ◽  
Piotr Kokoszka ◽  
Jane-Ling Wang ◽  
Yichao Wu
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
High Dimensional ◽  
Special Issue
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