Penalized least squares for single index models

2011 ◽  
Vol 141 (4) ◽  
pp. 1362-1379 ◽  
Author(s):  
Heng Peng ◽  
Tao Huang
Keyword(s):  
Least Squares ◽  
Penalized Least Squares ◽  
Single Index ◽  
Single Index Models

Nonlinear profile monitoring with single index models

2020 ◽  
Author(s):  
Takayuki Iguchi ◽  
Andrés F. Barrientos ◽  
Eric Chicken ◽  
Debajyoti Sinha
Keyword(s):  
Profile Monitoring ◽  
Single Index ◽  
Single Index Models

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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