scholarly journals Asymptotic properties of the first principal component and equality tests of covariance matrices in high-dimension, low-sample-size context

2016 ◽  
Vol 170 ◽  
pp. 186-199 ◽  
Author(s):  
Aki Ishii ◽  
Kazuyoshi Yata ◽  
Makoto Aoshima
Keyword(s):  
Sample Size ◽  
High Dimension ◽  
Asymptotic Properties ◽  
Principal Component ◽  
Covariance Matrices

scholarly journals Tests for covariance matrices in high dimension with less sample size

2014 ◽  
Vol 130 ◽  
pp. 289-309 ◽  
Author(s):  
Muni S. Srivastava ◽  
Hirokazu Yanagihara ◽  
Tatsuya Kubokawa
Keyword(s):  
Sample Size ◽  
High Dimension ◽  
Covariance Matrices

Robust centroid based classification with minimum error rates for high dimension, low sample size data

2009 ◽  
Vol 139 (8) ◽  
pp. 2571-2580 ◽  
Author(s):  
Jiancheng Jiang ◽  
J.S. Marron ◽  
Xuejun Jiang
Keyword(s):  
Sample Size ◽  
High Dimension ◽  
Error Rates ◽  
Minimum Error ◽  
Size Data

Functional Linear Regression

2018 ◽  
Author(s):  
Hervé Cardot ◽  
Pascal Sarda
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Estimation Error ◽  
Asymptotic Properties ◽  
Principal Component Regression ◽  
Principal Component ◽  
Penalized Least Squares ◽  
Open Problems ◽  
Functional Linear Regression

This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.

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