Miscellanea. Efficient estimation of additive nonparametric regression models

Biometrika ◽  
1997 ◽  
Vol 84 (2) ◽  
pp. 469-473 ◽  
Author(s):  
O. Linton
Keyword(s):  
Nonparametric Regression ◽  
Regression Models ◽  
Efficient Estimation ◽  
Additive Nonparametric Regression

EFFICIENT ESTIMATION OF GENERALIZED ADDITIVE NONPARAMETRIC REGRESSION MODELS

2000 ◽  
Vol 16 (4) ◽  
pp. 502-523 ◽  
Author(s):  
Oliver B. Linton
Keyword(s):  
Nonparametric Regression ◽  
Regression Models ◽  
Exponential Family ◽  
Efficient Estimation ◽  
Conditional Heteroskedasticity ◽  
Criterion Functions ◽  
Special Cases ◽  
Multiple Parameter ◽  
Additive Nonparametric Regression ◽  
New Procedures

We define new procedures for estimating generalized additive nonparametric regression models that are more efficient than the Linton and Härdle (1996, Biometrika 83, 529–540) integration-based method and achieve certain oracle bounds. We consider criterion functions based on the Linear exponential family, which includes many important special cases. We also consider the extension to multiple parameter models like the gamma distribution and to models for conditional heteroskedasticity.

ESTIMATING ADDITIVE NONPARAMETRIC MODELS BY PARTIAL Lq NORM: THE CURSE OF FRACTIONALITY

2001 ◽  
Vol 17 (6) ◽  
pp. 1037-1050
Author(s):  
Oliver Linton
Keyword(s):  
Asymptotic Normality ◽  
Rate Of Convergence ◽  
Nonparametric Regression ◽  
Regression Models ◽  
New Method ◽  
Kernel Estimators ◽  
One Dimensional ◽  
Nonparametric Models ◽  
Additive Nonparametric Regression ◽  
Consistency And Asymptotic Normality

We propose a new method for estimating additive nonparametric regression models based on taking the Lq median of a sample of kernel estimators. We establish the consistency and asymptotic normality of our procedures. The rate of convergence depends on the value of q. For q > 3/2 one has the usual one-dimensional rate, but if q ≤ 3/2 the rate can be slower.

Sign in / Sign up

Export Citation Format

Share Document